Kane opened his Bundesliga goalscoring account for the season with the winner against SV Elversberg on Sunday, having gone the first two matchdays without finding the net. He has been more prolific in cup competition, scoring three goals and adding an assist across his opening matches in the Champions League and DFB-Pokal.
Talks over a new deal have moved beyond initial statements of intent, with concrete figures now under discussion.
"Both sides are optimistic of reaching an agreement," Sport Bild reported.
Bayern are pushing for a contract running until 2029, with no reduction expected to Kane's current top-level salary should he sign, but two significant points remain unresolved.
The first concerns the length of any new deal. Kane has his sights set on playing at the 2030 World Cup and would prefer terms that run through that tournament, while Bayern's initial preference has been for the shorter 2029 date.
Given Kane turns 33 this year, extending his contract all the way to 2030 would mean Bayern committing to a forward who will celebrate his 37th birthday just a week after that World Cup final, a significant outlay given his salary is reported to sit around €25 million per year, which could see the overall value of an extension reach €100 million.
The second sticking point concerns an exit clause similar to the one already included in Kane's current contract, which the 121-cap England international is expected to retain in any new deal.
Bayern Munich, for their part, are likely to insist on tightening the terms around any such clause, wanting confirmation that a decision to trigger it in the summer would need to be announced by January 31 at the latest, mirroring the structure of his existing agreement.
Kane's current deal, signed when he joined from Tottenham Hotspur in 2023, is due to expire at the end of the 2026-27 season. His release clause under that contract has already lapsed, having only been active until the end of January this year, giving Bayern greater control over his situation as negotiations continue. Since arriving in Munich, Kane has finished as the Bundesliga's top scorer in each of his first three seasons, a record that underlines why the club are so determined to tie him down for the coming years regardless of his advancing age.