Here's a long interview/profile of Stephen Colbert, discussing where his show is right now. Where he is right now is that his show is profitable but not as much as CBS was hoping it would be.
From my vantage point as a viewer, it's an increasing disappointment, though this week there are moments that remind you how good he can/could be. Last night, there was a great opening with Laura Benanti expertly playing Melania Trump and a good spot with Keegan-Michael Key. Still, I got the sense that once he doesn't have the Republican Convention (or next week, the Democratic one) to talk about, it'll be back to "So, tell me about this new movie you have opening this weekend."
The article alludes to the rumor that CBS wants to flip the time slots of James Corden's show and Colbert's. I really, really doubt this will happen. Some folks discussing this possibility seem to not take into account that Colbert almost certainly has time slot protection in his contract…a clause that says his show will air at 11:35. That's very standard for talk show hosts these days and Colbert's agent also represents Jimmy Kimmel and I think a few others. Much of the mess with the Conan O'Brien Tonight Show came about because O'Brien's agents had neglected to secure that for him, leaving NBC the option of shifting him to a later time. No agent or lawyer who represents a late night host will ever make that mistake again.
That doesn't mean that CBS couldn't propose it to Colbert but I would think he'd say no and they'd have to leave him right where he is or cancel him. I doubt they're ready to take that drastic step.