Prospective Coaches are going to be named by everyone from those on the boards to media. As long as LSU officials say nothing there's no problem. Good candidates will love the attention and know how to handle it. Those who can't are the ones we don't want. If LSU makes comments on coaches then our fears of them screwing it up will be realized.
You can't stop the media from speculation in this world of 24/7 instantaneous news and information technology. Coaches know they have to deal with this. There's nothing LSU can do to stop it.