The bid comes after Spurs chairman Daniel Levy has reportedly knocked back bids from the German giants, with reports prior to today suggesting the clubs were still some £20 million apart in their valuations.
Bayern's offer for Kane is worth more than €100 million (£86 million) with add-ons included, according to Sky Germany.
However, Spurs have been demanding in excess of £100 million - closer to €120 million - for the England captain.
Kane is not pushing for a move away from the club and is said to be happy to stay on for the season should a bid not be accepted before next weekend's Premier League opener against Brentford.
However, the player has just a year left on his contract and currently has no intention of signing a new deal.
Kane has also reportedly already agreed personal terms earlier this summer with Bayern.
Bayern believe they have improved on their previous bid and feel their latest proposal is fair and final. It is suggested they will pursue other targets should Tottenham reject this approach.
Kane is Tottenham's all-time record goalscorer with 280 goals in 435 appearances, having scored his first Spurs goal in December 2011.
He has scored 213 goals in 320 Premier League games and is currently 48 goals off breaking Alan Shearer's record as the highest scorer in Premier League history.
Should the England captain stay on with Spurs for this season, he may well spark a bidding war for his free transfer once he is out of contract next summer, with the likes of PSG, Real Madrid and Manchester United all ready to join the queue next June.
