Bayern Munich will go after Harry Kane with all their might because they really need Harry Kane to strengthen the team they have, at least with Harry Kane's old age maybe he can follow the flow of the game and the instructions given can be done well so you can say Bayern Munich prefer players with pretty good emotional control and above average skills.
Is Mane not enough for Munich? I'm just worried that Kane will just be a backup. Indeed he wants to win in the league, because Tottenham have not given him that. But maybe if he intends to leave Tottenham will not let him go cheap and easy. I think Kane could choose Madrid, because maybe Anceloti will start looking for a replacement for Benzema.
Mane may not be enough for Bayern Munich considering his performance since leaving Liverpool to the German Champions Bayern Munich and considering his injury state I think just like Real Madrid who's going to get a supporting striker or a replacement for Benzema Bayern Munich needs to bring Harry Kane to the team to play along with Mane I believe they both can pair together with Kane up front and Mane play as a supporting striker. Kane May likely move to Bayern Munich as a free agent when his contract expires with Tottenham because the striker may not be allowed to leave to another club since his presence is still needed in the club regardless of their trophyless state since joining the club.