The first bid of €70 million plus add-ons was rejected by Spurs last month, but the German champions have now upped their offer and are waiting for a response.
Kane has a year left on his current contract with Tottenham, and the club is hoping to convince him to extend it.
However, Bayern are in the market for a new forward this summer, and head coach Thomas Tuchel has already discussed a potential move with Kane.
Manchester United has long been interested in Kane, and current boss Erik ten Hag is also a known admirer.
Meanwhile, Real Madrid head coach Carlo Ancelotti reportedly told the club’s board that he wanted to sign Kane at a key meeting to discuss transfers.
Kane’s contract negotiations with Tottenham were put on hold last season, as the striker focused on helping the club return to the Champions League.
However, Spurs missed out on European football altogether after an eighth-placed finish.
Despite not winning a trophy at domestic or international level, Kane is highly regarded for his abilities as a chief goalscorer and creator for club and country.
He broke Jimmy Greaves’ all-time Tottenham goalscoring record in February and became England’s record goalscorer the following month.
Bayern’s interest in Kane is understandable, given his versatility as a striker. He is not just a prolific goalscorer but also adept at holding the ball up and playing in fast runners.
Kane’s ability to create depth by dragging defenders out of the back line would greatly enhance Tuchel’s possession game.
In short, Kane would be an excellent addition to Bayern’s already impressive squad, and it remains to be seen whether Tottenham will be able to convince him to stay or if he will be tempted by a move to Germany.