The England captain is expected to sign a new agreement after the international break, with Bayern prepared to offer him a contract running until at least 2029.
The proposed length would be unusual for a player of Kane's age, but Bayern supervisory board member Karl-Heinz Rummenigge has already defended the decision to make an exception for the club's leading goalscorer.
Kane is also insisting on an exit clause in his new contract, with Fabrizio Romano reporting that this remains one of the points still being discussed.
The clause would be limited and designed to give Kane the possibility of returning to the Premier League. There is also expected to be a separate provision giving his former club Tottenham Hotspur a matching right.
Despite those details still being negotiated, Romano does not view them as an obstacle to the overall agreement.
“It is getting really, really close. I think it will happen, it is imminent,” Romano said.
Kane's desire for a potential Premier League return would give the new contract an unusual feature, allowing the 33-year-old to secure his long-term future in Munich while retaining a route back to England.
For Bayern Munich, the willingness to offer a deal through at least 2029 represents a significant commitment to a striker who has continued to be central to the club's plans.
The remaining discussions therefore concern the structure of Kane's exit options rather than whether he will stay. According to Romano, the extension is now approaching its final stages, with a new Bayern contract expected after the international break.