I don't think this player would fit in Bayern's squad, he is more suited to the English style of play and Bayern are currently tossing from side to side due to problems with the lack of a good striker. And besides as you said it will be difficult to convince him to move and most likely money won't influence the deal, Kane is a man of principle
Judging from his condition at Tottenham, it's clear for now I'm not too sure if he will move because Tottenham's current performance is quite good even though the target for the title is still very difficult.
On the other hand Tottenham a few seasons before could resist Kane's desire to move with a modest squad but now their squad is complete enough and still able to compete at least in the top 4 so I don't think he will leave in this condition.