Rumors keep kicking up that CBS will give “The Late Show With Stephen Colbert” to James Corden.

A TV insider told Page Six on Wednesday, “There’s talk they will move ‘The Late Show’ to LA — and replace Colbert with James Corden.”

But insiders close to “The Late Show” countered that Colbert’s job is safe. And a source exclusively told Page Six that “The Late Show” is not moving to LA — but that Colbert’s producers are exploring taking the show to LA for a week of remote shows with Colbert.

“They are just exploring going to LA for a week with Colbert,” the source explained. Colbert’s producers have been calling around to different venues in LA to accommodate “The Late Show,” we hear — including the Hollywood Pantages Theatre. But plans are preliminary.

Hollywood first began buzzing last summer that Corden could replace Colbert. An insider told us, “They have been talking about this for a long time, but there’s no chance it could happen before next fall. The talk is that CBS would offer Colbert the chance to do an edgier show at 12:30 a.m., which he is actually more suited to.”

But both Corden and CBS brass have adamantly denied the possibility. Corden told Howard Stern that it’s “never gonna happen,” and said to Variety, “I just think it’s silly.” CBS exec Glenn Geller told The Hollywood Reporter, “We have no plans to flip the two shows.”

Since the summer, Corden’s career has gotten hotter. He’s been picked to host the Grammys after his Carpool Karaoke segment has attracted the likes of Adele, Lady Gaga, Justin Bieber and, on Wednesday night, Madonna.

But CBS has crowed that Colbert’s ratings have been on the rise. The network’s Les Moonves said at a UBS conference this week, “We now have Colbert and Corden, both are doing extraordinarily well. Colbert had a little bit of a rocky start, but his ratings are going way up, and James Corden has become an internet sensation. So both of them are very profitable, which wasn’t the case in the latter years of Letterman and our 12:30 show.”