Saban told ESPN.com on Saturday that he "never considered" leaving the Crimson Tide for the Longhorns.
"The way this sort of got spun, it was a little bit more like, 'OK, he got a new contract at Alabama, so he's going to stay at Alabama instead of going to Texas,'" Saban said. "That wasn't even a conversation.
"I knew that if Mack stepped down, there would probably be an opportunity, but it wasn't something I was interested in doing, not at this stage in my career."
Saban has returned Alabama to the top of college football by winning three BCS national championships in four seasons, and he would probably be playing for another if not for the 109-yard return of a missed field goal for a touchdown by Auburn cornerback Chris Davis in the Iron Bowl.
For his part, Saban believes Brown has earned the right to go out on his own terms.
"Mack Brown is the coach at Texas," Saban said. "He deserves the right, based on his body of work, to be able to leave the program the way he wants to leave the program."
And now that he is stable and settled in his situation at Alabama -- "I don't want to go someplace else. I don't know how many times I can say that," Saban said -- Saban will almost certainly get to do just that with the Crimson Tide.