What will Conan O’Brien do?

? If “Tonight” show host Conan O’Brien decides he doesn’t want to shift back to a later time slot at NBC, Fox executives have a clear message for him: We love you.

“It’s a very compatible fit for our brand,” said Kevin Reilly, Fox’s entertainment president, on Monday. “He’s one of the few guys on the planet who has demonstrated he can do one of these shows every night.”

And to make the point even clearer, Reilly, a former NBC executive, said, “I love Conan personally and professionally.”

NBC’s late-night shuffle, one of the most compelling dramas this television season, hinges on whether O’Brien will accept what is effectively a demotion or go to a network with a spotty record developing a late-night show. NBC confirmed it was ending Jay Leno’s prime-time show to mollify angry affiliates. He would appear at 10:35 p.m. CST, followed by O’Brien under the “Tonight” show banner a half hour later.

O’Brien had waited five years after being promised the “Tonight” show and its time slot after the late local news, moving his family and staff from New York to California. That chance lasted half a year. A spokeswoman for O’Brien did not return a request for comment on Monday, and NBC said it has not heard a decision from the comic.

NBC Universal Television Entertainment Chairman Jeff Gaspin said he had given Leno, O’Brien and Jimmy Fallon (whose show would start at 12:05 a.m.) the weekend to think about the plan.

“I would love the three of them to stay at NBC,” Gaspin said.

O’Reilly said there have been no negotiations with O’Brien or his representatives over a move.

Fox could potentially offer a 10 p.m. time slot, giving O’Brien the jump on both Leno and David Letterman.