The bid was said to be Bayern's "final offer" for the England captain, with the German giants understood to have expected it would be accepted.
They also claimed they would move on to other targets if no agreement was reached, with reports suggesting their most recent offer exceeded €100 million (£86 million).
Kane, who has 280 goals in 435 appearances for Tottenham in all competitions, captained Spurs in Sunday's pre-season match against Shakhtar Donetsk and scored four goals.
He waved to the home crowd at the end of the match, with some interpretations believing it to be a farewell gesture.
The England striker is keen to have his future sorted before Tottenham's opening Premer League fixture against Brentford this weekend and is reportedly happy to stay with the London club this season.
As it stands, he is unlikely to sign a new contract and could conceivably leave for free next summer.
However, neither party have completely walked away from the negotiations, according to Sky Sports.
Kane is currently with Spurs in Barcelona for their final pre-season friendly ahead of the new season.
