The German star, who is at Euro 2024 with his teammates, may be ready to leave the club.
Kimmich has been at Bayern for many seasons, but may be moved on if they can secure Joao Palhinha from Fulham.
Speaking to Give Me Sport, journalist Ben Jacobs said: "I think we have to keep an eye on Liverpool, Juventus, possibly Barcelona, although there's obviously financial considerations, and even Manchester United, who all could be in the race for Kimmich and are all assessing whether there's value at that number before making any kind of meaningful approach.
"Kimmich's future will also be intertwined to some extent with Joao Palhinha. Should he come in as a new defensive midfielder and that deal get done with Fulham, it might end up costing close to £60m, and almost certainly €60m at the lower end.
"So you know, ranging between £50m if maybe Bayern eventually get their way, and £60m if Fulham get their price and if Palhinha joins, then the expectation is it will further call into question Kimmich's future."