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.
Jurgen Klopp reportedly will choose to rest after resigning as Liverpool manager, and in the near future he has no plans to coach any club, including Bayern Munich. It's true, Jurgen Klopp doesn't seem to be going to coach the club that was once his rival, because he wants to respect Dortmund. Maybe Jurgen Klopp will completely rest for the next season or two, before returning to coaching one of Europe other elite clubs. Barcelona has also been rumored to be interested in recruiting Jurgen Klopp, but even if Jurgen Klopp is interested, it will not happen next season.
Meanwhile, on the other hand, if Bayern Munich appoints Vincent Kompany as Tuchel's next successor, it looks like they will not have many choices after receiving three rejections from three different managers. Vincent Kompany does have the potential to become a great manager if he gets the opportunity to coach a club as big as Bayern Munich, but his challenge next season is to compete with clubs like Leverkusen. Competition in the Bundesliga next season will be very competitive, Bayern Munich must be wise enough in choosing their next manager.