With Vaughn as a guest on "The Late Show," Letterman took the approach of presuming the relationship, which has been frequently photographed, but not "officially" confirmed.
"Hey, nice going on that Jennifer Aniston thing," the late-night host says to Vaughn on a taped interview to air Friday on CBS (11:30 p.m. EDT).
Letterman also tells Vaughn, who stars with Aniston in the upcoming film, "The Break-Up," that he thinks they make a nice couple.
An embarrassed and amused Vaughn responds: "It's very nice of you to say that, Dave, thank you. Yeah, it's been kind of interesting for me, and I just choose not to talk about my private life that much publicly."
As the conversation continues, the 36-year-old actor eventually addresses the audience, "Do you like the way he just kind of takes the approach that it's fact?"
Letterman then asks if they aren't a couple.
"I'm not saying we are or aren't a couple," says Vaughn. "I think she's great, but I just don't discuss whether we are."
Reports of a relationship between Vaughn and Aniston, 37, began to surface last fall when the two were shooting "The Break-Up." Neither star has confirmed it.
Aniston was divorced from Brad Pitt last October.