The 22-year-old has been linked with a possible move to the Premier League to link up with former manager Pep Guardiola, but the player's agent Uli Ferber has revealed that he has had discussions with Bayern's CEO to extend his stay at the Allianz Arena beyond 2020.
"In the summer Karl-Heinz Rummenigge came to us for the first time to discuss whether we can extend our association," Ferber told SportBild.
"We sat down together for the first time in the fall and will again one more time by the end of the year to lead the discussions.
"There is much to support an agreement given Kimmich's star has continued to rise."
"It was an incredible experience," he told Bild. "He is also very detail-orientated, very creative and puts big demands on his players.
"What he knew about the opposition and the way he practiced formations was impressive. My team-mates were always exactly where Pep Guardiola had prophesised."
In the same interview, Kimmich also played down the speculation he could leave Munich, saying he is not worried about his club situation.
"Since my Bayern contract runs until 2020, I don't have to worry," he said.
"When it comes to changing clubs, there are always two scenarios: either the club wouldn't want me anymore, or I'd want to try something new and gain a new experience.
"But, as I said, that's not currently an issue for me."