According to The New York Times, other possible VP picks for Clinton include Ohio Senator Sherrod Brown, Secretary of Labor Thomas E. Perez and Massachusetts Senator Elizabeth Warren.
Pictures of Julian Castro and Hillary Clinton together:
Julian Castro on becoming Clinton's VP: 'That's not going to happen'
SAN ANTONIO, TX - OCTOBER 15: Secretary of Housing and Urban Development Secretary Julian Castro introduces Democratic presidential candidate Hillary Clinton at a 'Latinos for Hillary' grassroots event October 15, 2015 in San Antonio, Texas. The event was part of the campaign's ongoing effort to build an organization outside of the four early states and work hard for every vote. (Photo by Erich Schlegel/Getty Images)
US Housing and Urban Development (HUD) Secretary Julian Castro speaks at the National Fair Housing Training and Policy Conference at the Housing and Urban Development Department in Washington, DC, on September 2, 2015. AFP PHOTO/NICHOLAS KAMM (Photo credit should read NICHOLAS KAMM/AFP/Getty Images)
WASHINGTON, DC - MAY 04: The Honorable Julian Castro and Eva Longoria, actress and co-founder, Latino Victory, attend the Latino Victory Foundation's Latino Talks event at The Hamilton on May 4, 2015 in Washington, DC. (Photo by Paul Morigi/WireImage)
Former US Secretary of State Hillary Clinton talks with Housing and Urban Development Secretary Julian Castro after taking part in a discussion on 'our nation's urban centers,' and 'challenges from housing and transportation to education and workforce accessibility' at the Center for American Progress (CAP) in Washington, DC, on March 23, 2015. AFP PHOTO/NICHOLAS KAMM (Photo credit should read NICHOLAS KAMM/AFP/Getty Images)
UNITED STATES - MARCH 11: Chairman Susan Collins, R-Me., introduces HUD Secretary Julian Castro, center, to Sen. Jack Reed, D-R.I., ranking member, before a Senate Appropriations Transportation, Housing and Urban Development, and Related Agencies Subcommittee hearing in Dirksen Building on FY2016 budget estimates for the Housing and Urban Development Department, March 11, 2015. (Photo By Tom Williams/CQ Roll Call)
Julian Castro, secretary of U.S. Housing and Urban Development (HUD), speaks during a House Financial Services Committee hearing in Washington, D.C., U.S., on Wednesday, Feb. 11, 2015. The hearing was entitled 'The Future of Housing in America; Oversight of the Federal Housing Administration.' Photographer: Andrew Harrer/Bloomberg via Getty Images
WASHINGTON, DC - AUGUST 18: U.S. Vice President Joe Biden (R) swears in Secretary of Housing and Urban Development Julian Castro (L) as his wife Erica and daughter Carina look on during a ceremonial swearing in ceremony in the Eisenhower Executive Office Building August 18, 2014 in Washington, DC. Castro, the former Mayor of San Antonio, Texas, was officially sworn in on July 28. (Photo by Win McNamee/Getty Images)
U.S President Barack Obama, right, gestures to Julian Castro, secretary of U.S. Housing and Urban Development (HUD), as they arrive to speak at the Department of Housing and Urban Development in Washington, D.C., U.S., on Thursday, July 31, 2014. Castro, the former San Antonio, Texas mayor, was sworn in this week and will begin his duties on Monday, Aug. 4. Photographer: Andrew Harrer/Bloomberg via Getty Images
UNITED STATES - JUNE 17: San Antonio Mayor Julian Castro testifies at a Senate Banking, Housing and Urban Affairs Committee hearing in Dirksen Building on his nomination to be Secretary of Housing and Urban Development, June 17, 2014. (Photo By Tom Williams/CQ Roll Call)
INDIANOLA, IOWA - SEPTEMBER 15: San Antonio Mayor Julian Castro speaks at the 36th Annual Harkin Steak Fry on September 15, 2013 in Indianola, Iowa. Sen. Harkin's Democratic fundraiser is one of the largest in Iowa each year. (Photo by Steve Pope/Getty Images)
CHARLOTTE, NC - SEPTEMBER 05: First lady Michelle Obama talks with San Antonio Mayor Julian Castro (C) and his brother Joaquin Castro during day two of the Democratic National Convention at Time Warner Cable Arena on September 5, 2012 in Charlotte, North Carolina. The DNC that will run through September 7, will nominate U.S. President Barack Obama as the Democratic presidential candidate. (Photo by Alex Wong/Getty Images)
CHARLOTTE. NC - SEPTEMBER 4: Democratic National Convention keynote speaker San Antonio Mayor Julian Castro (D) addresses the 2012 Democratic National Convention at the Time Warner Cable Arena in Charlotte, North Carolina. (Photo by /The Washington Post via Getty Images)