On a deal to 2027, the former Tottenham striker has been linked with a return to the Premier League next summer.
Those rumours have been rejected by Bayern chief Christophe Freund - and now Kane has declared he'd be keen to discuss fresh terms.
"In terms of staying there longer I could definitely see that," Kane said. "The Premier League, I don't know.
"If you had asked me when I first left to go to Bayern, I would have said for sure I would come back.
"Now I have been there a couple of years I would say probably say that has gone down a little bit, not so much, but I wouldn't say I would never go back.
"Right now I am fully all in with Bayern. I am extremely happy there, my wife and kids are happy to stay.
"I don't think there is any need to rush. The manager (Vincent Kompany) is a big part of that. I love the manager, I think he is fantastic. As long we are improving and I am improving then I am happy to see what we can achieve."
Kane added: "I think MLS is too early for sure the way I feel right now, the way I am playing right now. The MLS would be something later in my career when I am thinking about the last couple of years or so."