Originally Published: 20 APR 23 06:36 ET

Updated: 20 APR 23 07:50 ET

By Issy Ronald, CNN

(CNN) -- Woody Harrelson has confirmed Matthew McConaughey's claim that they might be brothers, saying "there is some veracity to that thought," during an appearance on "The Late Show with Stephen Colbert."

"We want to go and (do a DNA) test, but for him, it's a much more big deal," Harrelson said. "I mean he feels like he is losing a father. But I'm like, no, you're gaining a different father and a brother."

Like McConaughey, Harrelson recalled a conversation with "Ma Mac, Matthew's legitimate mother," when she told them that she "knew..." Harrelson's father.

"It's crazy. We were in Greece watching the US team win the World Cup and I mentioned something about regrets," Harrelson said. "And I said, 'You know, it's odd that my father has no regrets.' And I have known Ma Mac a long time, and she goes, 'I knew... your father.' And it was the ellipses I found a little troubling, or interesting."

Her pause, Harrelson added, was "filled with innuendo." Colbert quipped that it might even have been a "pregnant pause."

Last week, McConaughey said in the podcast "Let's Talk Off Camera with Kelly Ripa" that Harrelson's father was on furlough at the same time his own parents were undergoing their second divorce and that his mother and Harrelson's father could have met in West Texas.

Similarly, Harrelson told Colbert: "The year of [Matthew's] birth, nine months before, she was on a sabbatical from her relationship with his supposed father, Jim."

The "True Detective" stars are about to appear in the comedy series "Brother From Another Mother" for Apple TV+, a fictionalized portrayal of their own decades-long friendship, which began after they met in 1997 while working on Ron Howard's "EDtv."

Harrelson is also set to appear in the HBO series "White House Plumbers" alongside Justin Theroux, who told Entertainment Tonight he wouldn't be surprised if McConaughey and Harrelson turned out to be half-brothers. (CNN and HBO share parent company Warner Bros. Discovery.)

"I can't tell whether it's just, like, their sort of slow Southern and Texas drawls or I think Texas figures in there somewhere," Theroux said. "It's just a mentality. They're both so wonderfully sort of blissfully relaxed all the time."