I can't really tell how serious Bayern Munich are concerning this deal, for now they are just speculations which seem unlikely to me. Harry Kane has always been a die-hard Tottenham player it will take a mind blowing offer to convince him to switch sides and join Bayern Munich. Bayern Munich are in need of a striker but I think Tottenham also need his services and might not be open to letting him go this January.
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