I actually don't think it will. I think if Texas replaces Mack Brown this year with a major name, you can probably close the book on Saban rumors.
Unlike a lot of people here, I believed (and still do) the original report months back that Jimmy Sexton had told Texas that Saban would consider going to UTex if "something changed" in Tuscaloosa, and that Texas was the only other school he'd consider.
Now, what has changed in Tuscaloosa? Pretty much nothing. That doesn't mean Saban hasn't listened to Texas (or more accurately, Sexton listened to Texas). But hiring a big-name coach is harder than most people will ever know, and the number of things that have to go right is pretty huge. I think Texas knows this is their window to make a splash hire, and if Saban is their top candidate, it's pretty much now or never. If they hire someone else and that guy stinks up the joint for 3-4 years, Saban really will be too old to consider it.
The only thing I would worry about, from an Alabama fan's perspective, is Mack Brown staying. Unfortunately for Mack, he's just not a great coach, and he is on the tail end of his career. But if he sticks it out for 1-2 years, we'll all be back here next year (and maybe even the next) talking about this same subject. The best thing for Alabama is for Texas to push Mack out and hire a young replacement. Once that's done, the list of things that could push Saban away goes back to the usual, later-career stuff: Grandkids, health concerns, NCAA trouble, etc. None of those seem to exist right now.