I think Hermann is tied to UH for the next several years and UH has a large buyout clause. But,the LSU faithful are desperate and would easily pitch in to pry him out of Houston. I don't think Petrino goes because he owes the AD big time for helping resurrect his career and giving him a second chance.
Strangely enough, the mention of Mike Gundy is quite interesting, but I doubt he leaves The Stool. Ed Orgeron is the interim coach, but he does not get the HC gig. He had great defenses at USC and served as an interim coach, but also had three losing seasons at Ole Miss as a HC. The LSU donors do not want him as HC.
Briles is interesting in that he could definitely light things up in Baton Rouge and would be a good pick with his ties to texas high school football. He got Baylor competitive in a pretty short period time and LSU wants to get back on top right now. And they might get him at a pretty good price too. Hermann and Briles, at this time, seem to be at the top of the short list.