Here’s the relevant excerpt about a run for future office:
Now with Trump on his way out and the GOP reckoning with Trumpism, Corker isn’t ruling out another run for office. He said that he has completed his self-imposed two-year sabbatical from public life, though his two terms in the Senate were enough to satisfy his desire to legislate.
His state's governorship is up in 2022, and obviously a wide-open presidential primary waits in 2024. Corker has never considered challenging Tennessee Gov. Bill Lee (R), according to a source familiar with his thinking.
Bob Corker would be DOA in a primary against Bill Lee, so it makes sense that he's not considering it. Lee has angered some parts of the base, but it's over the sorts of things that they would dislike Corker even more. For instance, Lee got some flack about a year ago for allowing refugees to resettle in Tennessee, citing his faith, and some feel that Lee has abused his powers in terms of covid restrictions (even though we have no statewide mask mandate, restrictions on businesses, or restrictions on private or religious gatherings). I can't imagine those people going for Corker, and I think Lee has pretty strong support other than that.