The England captain, 32, spoke to German public broadcaster Das Erste ahead of the DFB-Pokal final, in which Bayern Munich beat VfB Stuttgart 3-0 to complete a domestic double.
Kane has now scored 146 goals and contributed 33 assists in 147 competitive appearances for the club since joining from Tottenham Hotspur for £95 million in the summer of 2023.
On the prospect of a contract extension, Kane was measured.
"In terms of staying longer, I could definitely see that. I have not had those conversations with Bayern yet, but if they were to arise I am willing to talk and have an honest conversation. It depends of course on how things go next year or so, what we achieve together.
"We are in a fantastic period and I am not thinking about anything else."
On a return to the Premier League, which had long been framed as his likely next destination, Kane was more circumspect than at any point since his move to Munich.
"As for the Premier League, I don't know. If you had asked me when I first left to go to Bayern I would have said I would definitely go back. Now that I have been there for a couple of years I would say the chances have gone down a little, but I would not say I would never go back."
Kicker reported this week that concrete talks between Kane and Bayern have already taken place, with Bayern offering a deal until 2029 and Kane aiming for a three-year extension to 2030. His release clause, which had been set at around €65 million and activated in February, has now expired, leaving Bayern in a stronger negotiating position.
Honorary president Uli Hoeness dismissed reported Barcelona interest with characteristic bluntness.
"Barcelona don't have any money anyway," he told Das Erste.
Bayern president Herbert Hainer was equally clear. "There is no question that we want to extend Harry Kane's contract. I also believe that Harry wants to extend with us."
Kane will captain England at the World Cup this summer. Contract talks are expected to resume in earnest after the tournament.