Colbert fired back at Trump after he dismissed CBS' Sunday morning politics show Face the Nation as "fake news" and "Deface the Nation" in an interview with CBS journalist John Dickerson last week.
After a fiery takedown of the president, who has been nothing but good for his ratings, Colbert said, "The only thing your mouth is good for is being Vladimir Putin's (expletive) holster."
"I have had a chance to see the clip now," Pai told WPHT's Rich Zeoli, "and so, as we get complaints – and we've gotten a number of them – we're going to take the facts that we find and we are going to apply the law as it's been set out by the Supreme Court and other courts and we'll take the appropriate action."
However, the law — at least as it is currently written — would appear to be Colbert's side.
The Late Show, which comes on at 11:30 ET/PT, airs outside of what is called the "safe harbor" hours of 6 a.m. and 10 p.m., local time, at which point children could be watching TV. Plus, because his show is taped, the editors were able to bleep out the offensive language before broadcast.
"As a consequence, the Commission does not take action on indecent material (meaning sexually explicit or excretory content) aired between 10 p.m. and 6:00 a.m," the FCC website says. "In this way, constitutionally-protected free speech rights of adults are balanced with the need to protect children from harmful content."
Pai added that should his agency decide to penalize Colbert and CBS, it would likely be limited to a fine.
Two days after the inflammatory monologue, Colbert told his audience that while he doesn't regret insulting the president and would do it again, he "would change a few words that were cruder than they needed to be."