The England captain, who turns 30 on Friday, has entered the final year of his contract with the Lilywhites and has been strongly linked with an exit from North London throughout this summer.
Bayern are believed to be the current frontrunners for Kane's signature, and club president Herbert Hainer recently confirmed that the Bavarian giants are interested in signing Tottenham's talisman.
Tottenham's majority owner Joe Lewis - who was charged on Tuesday with insider trading by US federal prosecutors - is understood to have informed chairman Daniel Levy that Kane must be sold this summer if he does not sign a new contract.
Despite recent reports indicating that Kane would prefer a move to Manchester United this summer, as well as reported interest from Paris Saint-Germain, Bayern are believed to be increasingly confident that they can finalise a move to sign Tottenham's No.10.
Bayern are said to have already seen two bids for Kane rejected, including their second offer thought to be worth in the region of €80m (£68m).
However, according to Get Football News Germany, the Bundesliga champions are prepared to spend in excess of €100m (£86m) to secure the services of their top transfer target.
The report adds that Bayern chiefs are set to meet again with Levy to hold talks over a transfer fee, and there is growing optimism that a breakthrough in negotiations could be reached by the end of this week.
Kane is also said to have already agreed personal terms over a move to the Allianz Arena, while the striker's wife was spotted in Munich last weekend and is claimed to have been looking at properties in the Grunwald area of Munich.
Bayern head coach Thomas Tuchel has admitted that he is determined to sign a new centre-forward this summer, with the German giants still yet to find a replacement for Robert Lewandowski who joined Barcelona last summer.
Bayern's pursuit of Kane also comes at a time when the future of Sadio Mane is believed to be uncertain amid reported interest from Saudi Arabian club Al-Nassr.
Meanwhile, newly-appointed Tottenham boss Ange Postecoglou has insisted that Kane's situation at the club has not changed and he remains an integral member of his first-team plans going forward.
Kane has returned to London with the rest of the Spurs squad following their pre-season tour of Asia, after scoring in a 5-1 victory over Singapore side Lion City Sailors on Wednesday.
The striker is both Tottenham and England's all-time record goalscorer, netting 280 goals in 435 appearances for the former over a 14-year period, as well as scoring 58 goals in 84 international caps for the latter.