"As an American and one who goes abroad ... every customs agent around the world, when they see your passport, they ask about Trump," Damon exclusively told "Popcorn with Peter Travers" on Thursday. "They go, 'Is that real?' They are kind of bewildered by the entire thing. I have to admit I am too."
Damon said he always saw Trump as "very entertaining," but he never saw him in a presidential light.
"I'm kind of amazed we've arrived at this point," he said of the businessman's nomination for president. "I'm concerned."
Damon added that it was Brexit -- England voting to leave the European Union -- that really woke him up to Trump's chances of possibly becoming commander-in-chief.
"Trump actually could win," he said. "I don't think he has the temperament. I have a lot of Republican friends and a lot of my Republican friends I wish were the Republican nominee."
Damon added that he believes the "rigging" of the election system led Trump to become the Republican nominee.
"Trump is almost like a protest vote," he added. "'I want to vote against all of you in Washington, D.C.' ... but to think about the actual practicality ... just this thing he did yesterday with, saying 'Russia release the emails,'" he added, referencing Trump's press conference on Wednesday in Doral, Florida, where he said that he hopes Russia finds Hillary Clinton's deleted emails.
"It makes me nervous," he said. "It's a binary choice.... There's no way we can let this guy be the [president]. To let that dude have the nuclear football, are you kidding me? That's dangerous. He's impulsive and rash, and doesn't seem to think deeply about too many things."
Suffice it to say, Damon says he is voting for Clinton.
The candid conversation wasn't all serious. Travers also told Damon that while sitting down with former presidential candidate Bernie Sanders recently for an interview, Sanders raved about his love for "Bourne," the amnesiac operative Damon has played onscreen for almost 15 years.
"That's the real deal!" Travers said.
Damon said hearing that was "fantastic" and that he would hop on the phone with his acclaimed director the second he left the building.
"Jason Bourne" opens in theaters tomorrow.
Tune in tomorrow on ABC News Digital to read and see the full amazing interview between Damon and Travers on "Popcorn."