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.

"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.