Vincent Kompany doesn't feel like he would be a "great" manager. Bayern Munich isn't some new club and they are not really hard to get some managers, I mean getting some world famous level of manager is not a problem for them, like go convince Klopp if you want to.
However, Kompany hasn't been manager for a long time, he just managed Burnley as far as I know and there isn't really anything that makes sense there, it should feel like we are going to end up with nothing of value at all, we are going to probably see Kompany fail at that high level because he has never been there. Don't get me wrong, as a player he has been at high places but as a manager he hasn't been at high places and I think Bayern needs someone with experience.
Firstly, I don’t think Klopp will accept the offer to coach Bayern Munich that was their direct rivals while he was coaching Dortmund before becoming Liverpool’s managers, and for him to have decided to leave just like that means he may not take any club offer for now.
On the other hand; Vincent Kompany is not a bad coach, he haven’t coached a big team yet but his tactics are better just that they lack quality players that can help the team with extra effort.
I am expecting him to be a very competitive coach at Bayern Munich, he will give his best to overtake Alonso next season.