"I understand Michael," he added. "I know Michael. And I could see him doing it. And I would love to have Michael run. Honestly, I love the competition."
The New York Times reported earlier that day that Bloomberg was seriously considering a third-party bid for the White House.
According to the report, Bloomberg sees an opening for a centrist candidate like himself if Republicans nominate Trump or Sen. Ted Cruz (R-Texas) and Democrats went with Sen. Bernie Sanders (I-Vermont), a self-described democratic socialist. And the billionaire media mogul is reportedly willing to spend at least $1 billion to fund his own campaign.
Trump, the current Republican front-runner, said on Fox News that he would do well in a three-way race.
"I think I'd do very well against Michael. And I think I'd do very well frankly in a three-person race. It would be fine. But I would love to see Michael do that," he said.
See photos of Michael Bloomberg through the years
Michael Bloomberg through the years
'I love the competition': Donald Trump encourages Michael Bloomberg to run for president
344913 02: Bloomberg L.P. founder and CEO Michael Bloomberg poses for a portrait November 2, 1998 in the training room at his offices in New York City. (Photo by Chris Casaburi/Getty Images)
UNITED STATES - CIRCA 2000: Republican mayoral candidate Michael Bloomberg samples a slice of life at Francesco's Pizzeria on Third Ave. in Bay Ridge, Brooklyn. (Photo by Linda Rosier/NY Daily News Archive via Getty Images)
UNITED STATES - CIRCA 2000: Republican mayoral candidate Michael Bloomberg talks to passersby while campaigning at Broadway and W. 225th St. (Photo by David Handschuh/NY Daily News Archive via Getty Images)
UNITED STATES - CIRCA 2001: Republican mayoral candidate Michael Bloomberg exchanges high-fives with 7-year-old Matthew DePoalo while campaigning on Ditmars Blvd. in Astoria. (Photo by Andrew Savulich/NY Daily News Archive via Getty Images)
388464 18: Michael Bloomberg of Bloomberg News Service hosts a party before attending the annual White House Correspondents Dinner, April 28, 2001 in Washington DC. (Photo by Mark Wilson/Newsmakers)
NEW YORK, UNITED STATES: Michael Bloomberg, Republican candidate for New York mayor, speaks to the press in Brooklyn, New York, 26 September 2001. Bloomberg handsomely won the 25 September New York mayoral primary election to be the official Republican party candidate to replace New York Mayor Rudy Giuliani on January 1 next year, according to exit polls. AFP PHOTO Doug KANTER (Photo credit should read DOUG KANTER/AFP/Getty Images)
UNITED STATES - OCTOBER 26: Republican mayoral candidate Michael Bloomberg meets with the Daily News editorial board. (Photo by Pat Carroll/NY Daily News Archive via Getty Images)
Mayoral candidate Michael Bloomberg leaves the polling booth at PS 6 in Manhattan, NY. (Photo by Jennifer S. Altman/WireImage)
399131 02: Michael Bloomberg, the108th Mayor of the City of New York, gives his inaugural address January 1, 2002 at City Hall in New York City. (Photo by Getty Images)
UNITED STATES - CIRCA 2002: Mayor Michael Bloomberg chats with diners at the International House of Pancakes at 135th St. and Adam Clayton Powell Blvd. in Harlem, where he picked up the endorsement of the Rev. Calvin Butts. (Photo by Craig Warga/NY Daily News Archive via Getty Images)
NEW YORK, UNITED STATES: New York City Mayor Michael Bloomberg (C), and former New York Stock Exchange President William Johnston (R) listens to New York Stock Exchange Chairman Richard Grasso (R) on the bell podium before Bloomberg rang the opening bell to begin trading 02 January, 2002. AFP PHOTO Henny Ray ABRAMS (Photo credit should read HENNY RAY ABRAMS/AFP/Getty Images)
399944 03: New York Mayor Michael Bloomberg speaks at the swearing in of over 300 probationary firefighters January 22, 2002 at the Fire Academy on Randalls Island in New York City. The new class is the second to enter the academy since the World Trade Center attack, when the department lost 343 firefighters. The probationary firefighters will begin physical training and classroom instruction before being sent out to firehouses around the city., (Photo by Spencer Platt/Getty Images)
UNITED STATES - JANUARY 30: Mayor Michael Bloomberg makes his first State of the City address in the City Council chamber at City Hall. (Photo by Linda Rosier/NY Daily News Archive via Getty Images)
Mayor Michael Bloomberg cuts the ribbon to begin the opening of fall's Fashion Week in Bryant Park in Manhattan, NY. (Photo by Jennifer S. Altman/WireImage)
UNITED STATES - FEBRUARY 09: Mayor Michael Bloomberg stands amidst fire officials during funeral of Fire Lt. Kevin Pfeifer at St. Margaret's Church in Middle Village, Queens. Pfeifer, 42, who worked with Engine Co. 33 in lower Manhattan, was killed in the Sept. 11 terrorist attack on the World Trade Center. Bloomberg, attending his first firefighter funeral since taking office last month, eulogized the fallen hero and praised the bravery of all the firefighters who responded to the attacks. (Photo by Mike Albans/NY Daily News Archive via Getty Images)
401921 01: New York City Mayor Michael Bloomberg speaks at the unveiling of a fifty-foot high stainless steel tree by artist Roxy Paine March 5, 2002 in New York City's Central Park. The tree is one of five public artworks on display in Central Park sponsored by the Whitney Museum of American Art. (Photo by Mario Tama/Getty Images)
NEW YORK, UNITED STATES: New York Mayor Michael Bloomberg(L) and Attorney General John Ashcroft (R) look at memorial banners and posters in front of St. Paul's Chapel 09 April 2002 in New York City, before visiting ground zero at the site of the World Trade Center attacks. AFP PHOTO/POOL/Kathy WILLENS (Photo credit should read KATHY WILLENS/AFP/Getty Images)
403191 02: New York City Mayor Michael Bloomberg (C) and Fire Commissioner Nicholas Scoppetta (R) look on as a U.S. flag that once flew over Ground Zero is raised during a ceremony at City Hall Plaza April 1, 2002 in New York City. The flag was immortalized in a photograph by Thomas Franklin of three firefighters raising it amid the rubble of the World Trade Center after the September 11, 2001 terrorist attack on New York City. (Photo by Mario Tama/Getty Images)
UNITED STATES - MAY 28: Mayor Michael Bloomberg addresses the Republican State Convention at the Sheraton New York Hotel on Seventh Ave. (Photo by Andrew Savulich/NY Daily News Archive via Getty Images)
NEW YORK - JUNE 14: National Aeronautics and Space Administration (NASA) astronauts Dominic Gorie (L) and Frank Culbertson (R) present an American flag to New York City Mayor Michael Bloomberg (C) in honor of Flag Day June 14, 2002 in New York City. The flag was found at Ground Zero, the location of the World Trade Center in New York, and was flown into space in December 2001 aboard the NASA Space Shuttle Endeavor. Culbertson was onboard the International Space Station September 11, 2001 when the terrorist attacks occurred in the U.S. (Photo by Mario Tama/Getty Images)
NEW YORK - JULY 4: New York City Mayor Michael Bloomberg gets a Nathan's Famous hot dog after Takeru Kobayashi won Nathan's Famous Fourth of July Hot Dog Eating Contest at Coney Island July 4, 2002 in the Brooklyn borough of New York City. Kobayashi, who won last year, set a new world record by eating 50 1/2 hot dogs in twelve minutes. (Photo by Mario Tama/Getty Images)
NEW YORK, NY - MAY 10: New York City Mayor Michael Bloomberg (2nd R) speaks with an aide while announcing a new emergency notification system at a news conference overlooking Ground Zero on May 10, 2011 in New York City. Bloomberg, who was joined by politicians, federal officials and the heads of mobile phone companies, spoke of the system that will alert what to do in case of emergency to anyone with an 'enabled' mobile device within range of a cell phone tower. Part of a law passed by Congress five years ago, the service is scheduled to be available in New York City and Washington, D.C. by the end of the year and is expected in the rest of the country by mid-2012. (Photo by Spencer Platt/Getty Images)
NEW YORK, NY - SEPTEMBER 07: New York Mayor Michael Bloomberg (R) speaks at a press conference as construction continues at the World Trade Center site on September 7, 2011 in New York City. The National September 11 Memorial & Museum will feature two reflecting pools on the footprints of the twin towers. The memorial is scheduled to be dedicated on September 11, 2011, the tenth anniversary of the World Trade Center terrorist attacks. (Photo by Mario Tama/Getty Images)
WASHINGTON, DC - MARCH 02: (L-R) Los Angeles Mayor Antonio Villaraigosa, New York Mayor Michael Bloomberg and Chicago Mayor Rahm Emanuel participate in a forum about education in big cities at the Katzen Arts Center on the campus of American University March 2, 2012 in Washington, DC. Calling their municipalities 'city-states,' the mayors suppored the idea of individual school districts being able to compete with states for the $4.35 billion 'Race to the Top' grant program created by President Barack Obama. (Photo by Chip Somodevilla/Getty Images)
NEW YORK, NY - OCTOBER 31: New York City Mayor Michael Bloomberg (C) rings the opening bell of the New York Stock Exchange on the first day of opening since Hurricane Sandy October 31, 2012 in New York City. The storm has claimed several dozen lives in the United States and has caused massive flooding across much of the Atlantic seaboard. U.S. President Barack Obama has declared the situation a 'major disaster' for large areas of the U.S. east coast, including New York City, with widespread power outages and significant flooding in parts of lower Manhattan and elsewhere. (Photo by Allison Joyce/Getty Images)
NEW YORK, NY - MARCH 12: New York City Mayor Michael Bloomberg holds a large cup as he speaks to the media about the health impacts of sugar at Lucky's restaurant, which voluntarily adopted the large sugary drink ban, March 12, 2013 in New York City. A state judge on Monday blocked Bloomberg's ban on oversized sugary drinks but the Mayor plans to appeal the decision. (Photo by Allison Joyce/Getty Images)
NEW YORK, NY - NOVEMBER 06: New York City Mayor-elect Bill de Blasio speaks with outgoing Mayor Michael Bloomberg at City Hall on November 6, 2013 in New York City. It was the first meeting between the two since de Blasio's election victory the day before. (Photo by John Moore/Getty Images)
NEW YORK, NY - AUGUST 19: New York City Mayor Michael Bloomberg speaks at a press conference with United States Secretary for Housing and Urban Development Shaun Donovan (not seen), unveiling a Hurricane Sandy Recovery Report on August 19, 2013 in the Greenpoint neighborhood of the Brooklyn Borough of New York City. The report calls for strengthening the region's electrical grid, reinforcing coastline and protecting gas supplies. (Photo by Andrew Burton/Getty Images)
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Trump also predicted that Bloomberg would take more votes away from the Democratic nominee than himself. He pointed out that Bloomberg is known for his advocacy for stricter gun-control policies.
"He could very well hurt the Democrats," he said. "He's very, very anti-Second Amendment — very. And he's got a lot of other things. I think he'd hurt the Democrats, personally, but I'd love to see him in the race."
Trump had a similar message Sunday when he was asked about Bloomberg's potential campaign on CBS' "Face the Nation."
"I would love it. I know Michael very well. I would love to compete against Michael. And I know him very well," Trump said, according to the show's transcript. "And I think he might very well get in the race. And I would love to have him get in the race. ... He's very opposite on me with guns, and he's opposite on pro-life, and he's opposite on lot of things. So, I would love to have Michael get in the race."
Trump further described Bloomberg as a former, and possibly current, "friend."
"And Michael has been a friend of mine over the years. Perhaps we're not friends anymore," he said. "He's wanted to do this for a long time. And he never pulled the trigger, and we will see if he does right now. But I would personally love to compete with Michael Bloomberg."
The Republican front-runner had almost the exact same response on Sunday's "Meet the Press."
"Michael has been a friend of mine over the years. I don't know if we're friends anymore, frankly. But Michael has been a friend of mine," Trump told NBC's Chuck Todd, according to the show's transcript.
"I would love to have Michael Bloomberg run," he added. "I would love that competition. I think I'd do very well against it. I would love to see Michael Bloomberg run."