Speaking with reporters after Bayern's dominant 5-1 home win over Stuttgart in the Bundesliga season opener, Kane said negotiations had begun for a contract extension.
"The first meeting started last week," Kane said.
The 33-year-old forward is among the favourites for the Ballon d'Or, which will be awarded in his hometown of London in August.
Kane said "a lot of details" needed to be discussed but hoped to continue his stay at Bayern, who he joined in 2023 from boyhood club Tottenham.
"I'm 33. It's probably going to be, not my last contract. But it's a big contract for me to sign.
"They need to make sure I'm happy. They obviously need to make sure they're happy... There's no panic from either side.
"I'm sure we'll get to a point where both sides are happy."
Bayern have repeatedly said they would like to extend Kane's deal at the club, which expires at the end of this season.
The England captain scored 36 goals in 31 Bundesliga games last term, the third most in a German top-flight campaign, while winning the league and cup double.
In total, he scored 73 goals for club and country last season, including six at the World Cup as England made it to the semi-finals.