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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 will certainly not accept to be a coach of Bayern next season. He has said that no club and no national team next season, I believe he is a man of his words. He said that he retire from football activity, but he doesn't promise to stay retiring or comeback, but definitely not next season. Even if he comes back to coach a team, it will definitely be not Bayern, it will most probably be a national team.
I don't understand the reasoning of the idea of Bayern hiring Vincent Kompany. His best achievement is that he managed Burnley promoted to Premier League and then get them relegated back to Championship Division. He did never play for Bayern or even other Bundesliga team, he has no experience in Germany football at all. He may be a good coach, but not at Bayern level. This rumor makes me really confused.