George Clooney isn't taking chances traveling ahead of birth of his twins with Amal


George and Amal Clooney's twins are coming any day now!

The 56-year-old actor hinted that the due date for his babies was coming soon on Sunday, when he didn't appear at the Aurora Prize for Awaking Humanity event in Yerevan, Armenia, joking about Amal could give birth. George co-founded the event, which honors survivors of the Armenian genocide.

"I really would have been [there] but if I came there and my wife had twins while I was there, I could never come home," he said in a taped video message to the audience.

WATCH: EXCLUSIVE -- Amal Clooney to Give Birth to Twins 'Any Day Now,' Source Says

Last week, a source told ET that Amal is expected to give birth "any day now," though her due date was originally thought to be around the first week of June.

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Amal Clooney's pregnancy style
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Amal Clooney's pregnancy style
Amal Clooney arrives with Secretary-General of The United Nations Antonio Guterres at the UN Headquarters on March 10, 2017 in New York. / AFP PHOTO / ANGELA WEISS (Photo credit should read ANGELA WEISS/AFP/Getty Images)
Amal Clooney arrives to meet with Secretary-General of the United Nations, Antonio Guterres at the UN Headquarters on March 10, 2017 in New York. / AFP PHOTO / ANGELA WEISS (Photo credit should read ANGELA WEISS/AFP/Getty Images)
NEW YORK, NY - MARCH 09: Amal Clooney arrives at the United Nations on March 09, 2017 in New York, NY. (Photo by Josiah Kamau/BuzzFoto via Getty Images)
NEW YORK, NY - MARCH 09: Amal Clooney arrives at the United Nations on March 09, 2017 in New York, NY. (Photo by Josiah Kamau/BuzzFoto via Getty Images)
NEW YORK, NY - MARCH 09: Amal Clooney is seen on March 9, 2017 in New York City. (Photo by XPX/Star Max/GC Images)
Amal Clooney and Georges Clooney seen leaving their hotel in Paris, on February 26, 2017. (Photo by Mehdi Taamallah / Nurphoto)
Amal Clooney and Georges Clooney seen leaving their hotel in Paris, on February 26, 2017. (Photo by Mehdi Taamallah / Nurphoto)
PARIS, FRANCE - FEBRUARY 24: George Clooney and Amal Clooney arrive at the Cesar Film Awards 2017 at Salle Pleyel on February 24, 2017 in Paris, France. (Photo by Fran�is Pauletto/Corbis via Getty Images)
Pregnant Amal Clooney and Georges Clooney seen arriving at the Ritz hotel in Paris, on February 25, 2017. (Photo by Mehdi Taamallah/NurPhoto via Getty Images)
Pregnant Amal Clooney and Georges Clooney seen arriving at the Ritz hotel in Paris, on February 25, 2017. (Photo by Mehdi Taamallah/NurPhoto via Getty Images)
PARIS, FRANCE - FEBRUARY 24: George Clooney and Amal Clooney arrive at the Cesar Film Awards 2017 at Salle Pleyel on February 24, 2017 in Paris, France. (Photo by Fran�is Pauletto/Corbis via Getty Images)
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"They are expecting her to give birth early," the source said, noting that the couple is currently residing at their home in Sonning, England.

WATCH: Amal Clooney Shows Off Baby Bump in Chic Red Dress in London

In April, the two were snapped holding hands during a country walk in England, the always stylish Amal going casual and covering her baby bump in a green jacket.

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George Clooney through the years
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George Clooney through the years
US actor/movie maker George Clooney speaks during the global launch of 100 LIVES initiative and the announcement of a new humanitarian prize in New York on March 10, 2015. The 100 LIVES, initiated to express gratitude to individuals and institutions whose heroic actions saved Armenian lives during the Genocide 100 years ago, is to address the issues of genocide, human rights violations and the power of positive action. AFP PHOTO/JEWEL SAMAD (Photo credit should read JEWEL SAMAD/AFP/Getty Images)
THE FACTS OF LIFE -- Pictured: George Clooney as George Burnett -- Photo by: Ron Tom/NBCU Photo Bank
UNITED STATES - MAY 02: ROSEANNE - 'Let's Call It Quits' - Season One - 5/2/89, Roseanne has difficulty accepting new rules from a tough new supervisor at the factory. George Clooney (Booker) stars., (Photo by ABC Photo Archives/ABC via Getty Images)
George Clooney and Michelle Pfeiffer on phones in backseat of car in a scene from the film 'One Fine Day', 1996. (Photo by 20th Century-Fox/Getty Images)
ER -- SEASON 4 -- Pictured: George Clooney as Doctor Doug Ross (Photo by Sven Arnstein/NBC/NBCU Photo Bank via Getty Images)
NBC SUNDAY NIGHT AT THE MOVIES- COMBAT HIGH -- Pictured: (l-r) Keith Gordon as Max Mendelsson, George Clooney as Maj. Biff Woods -- (Photo by: Paul Drinkwater/NBC/NBCU Photo Bank via Getty Images)
THE TONIGHT SHOW WITH JAY LENO -- Episode 1404 -- Pictured: (l-r) Actor George Clooney during an interview with host Jay Leno on June 25, 1998 -- (Photo by: Margaret Norton/NBC/NBCU Photo Bank via Getty Images)
George Clooney, Mark Wahlberg And Ice Cube Star In 'Three Kings.' '99 Wb And Village Roadshow Film Limited (Photo By Getty Images)
1999 George Clooney stars in the latest season of 'ER.'
NEW YORK, NY - MARCH 02: Actor George Clooney attends SeriousFun Children's Network's New York City Gala at Avery Fisher Hall, Lincoln Center on March 2, 2015 in New York City. (Photo by Dimitrios Kambouris/Getty Images)
WESTWOOD, CA - DECEMBER 5: Actor George Clooney attends the 'Ocean's Eleven' Westwood Premiere on December 5, 2001 at the Mann Village Theatre in Westwood, California. (Photo by Ron Galella, Ltd./WireImage)
George Clooney (Photo by Vera Anderson/WireImage)
HOLLYWOOD - MARCH 31: Actor/director George Clooney arrives to the premiere of Universal Pictures' 'Leatherheads' held at Grauman's Chinese Theatre on March 31, 2008 in Hollywood, California. (Photo by Kevin Winter/Getty Images)
BERLIN, GERMANY - FEBRUARY 8: (L to R) Actors Natascha McElhone, Ulrich Tukur, George Clooney and director Steven Soderbergh attend the 53rd Berlinale Film Festival February 8, 2003 in Berlin, Germany. Their new film 'Solaris' was written and directed by Soderbergh. (Photo by Kurt Vinion/Getty Images)
David Strathairn and George Clooney during 2005 Venice Film Festival - George Clooney - Sighting in Venice Lido, Italy. (Photo by George Pimentel/WireImage)
US actor and director George Clooney (R) and co-star Renee Zellweger arrive in London's Leicester Square on April 8, 2008 to attend the European Premiere of the film, Leatherheads directed by Clooney. AFP PHOTO / Max Nash (Photo credit should read MAX NASH/AFP/Getty Images)
LOS ANGELES - NOVEMBER 14: Actor George Clooney speaks to the media at the Four Seasons Hotel on November 14, 2006 in Los Angeles, California. (Photo by Piyal Hosain/Fotos International/Getty Images)
Nominee for Best Actor ('Michael Clayton') George Clooney (R) and gilrfriend Sarah Larson arrive for the 80th Annual Academy Awards at the Kodak Theater in Hollywood, California on February 24, 2008. AFP PHOTO / STAN HONDA (Photo credit should read STAN HONDA/AFP/Getty Images)
Actor George Clooney speaks during the 80th Annual Academy Awards held at the Kodak Theatre on February 24, 2008 in Hollywood, California. (Photo by Kevin Winter/Getty Images)
Matt Damon and George Clooney (Photo by Lester Cohen Archive/WireImage)
George Clooney and Julia Roberts during 11th Annual Critics' Choice Awards - Backstage and Audience at Santa Monica Civic Auditorium in Santa Monica, California, United States. (Photo by Chris Polk/FilmMagic)
George Clooney at junket for 'Good Night and Good Luck,' a new movie. (Photo by Michael Albans/NY Daily News Archive via Getty Images)
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