The Level of performance the Bayern Munich will gain if their acquired Harry Kane is insane and Thomas Tuchel surely knows about this things, and he is likely putting up his play on the top of his head while creating the best team possible this season, right now if they can still add Sadio Mane to the group then that will be a great thing for Tuchel and Bayern Munich but if Thomas Tuchel couldn't save Sadio mane from getting out of the Bayern Munich then the possibility that they will move on without him is a possibility aswell,
of course if Bayern Munich will fight for Harry Kane because Kane's performance is very good and Bayern Munich officials know this. I'm not sure Mane is the best player at the moment, while the performance he gave last season was not optimal, so Bayern Munich might think about letting Mane go and try to pursue Harry Kane to be added to Bayern Munich's formation.
this is all done because Bayern Munich seems to have a desire to compete hard in the champions league so they want to get reliable players to be able to perform well in the champions league later.