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.
Even if Kane goes to Bayern Munich, the club will still have another problem on how to play him with other forwarders. That was the problem Bayern Munich faced on how to play without Lewandowski and they have solved the problem and they can score so many goals in one match. If they bring Kane, there is no doubt that he will later adapt but there will be problem in the team.
So it will be fine that if Bayern wants to sign a striker, they should do so when the seasonhas ended so that there will be time for preseason.