Incoming CNN president Jeff Zucker and TBS “Conan” host Conan O’Brien have a long and not particularly friendly history.

When they were both students at Harvard University, O’Brien ran the Harvard Lampoon humor magazine, while Zucker was editor of the Harvard Crimson, the venerable student newspaper. O’Brien organized a prank in which the Lampoon staff stole all the copies of a new edition of the Crimson. Zucker responded by calling the cops on O’Brien.

They would work together in a relatively friendly fashion for years at NBC, as Zucker rose through the ranks as an executive, and O’Brien toiled away on “Late Night.” Then got the best gig in late night, as host of “The Tonight Show.” That all came crashing down in 2010, when Jay Leno was moved out of primetime, returned to late night and O’Brien left NBC — all after just seven months. Zucker maintains that it was the decision of NBC entertainment chief Jeff Gaspin, but it is well known that he had the final say in the decision, which permanently spoiled any goodwill between the two men.

Now, with Zucker taking over CNN, he will once again be in the same corporate family as O’Brien, whose TBS show is one of the channel’s trademark programs.

Coincidentally O’Brien recently debuted an online-only chat show called “Serious Jibber-Jabber with Conan O’Brien.” The series sees O’Brien in extended interviews with notable people, and there is minimal joking around. A source at TBS suggested that CNN might be a good fit for such a show, if O’Brien wanted to migrate it from the Web to TV, maybe late at night on the weekend. CNN already re-airs documentaries from sister network HBO, so it wouldn’t be a huge stretch.

With Zucker taking the helm at CNN, the possibility of any such plan is likely DOA.