The Manchester City winger has been the subject of speculation that the Bundesliga champions will make a move to bring him back to Germany in the off-season.
However, Bayern president Uli Hoeness said earlier in the week that a deal was unlikely because of the “insane sums” it would require.
Speaking to BILD, Kimmich made no secret of the fact that he would like to see the 23-year-old in Bavaria next season, despite Hoeness’s comments.
“I would like to have Leroy at Bayern, that would send the right message,” he said.
“He is a player who would be a good fit at Bayern. I think he is a very good player.
“But it's his decision and the task of those responsible to convince him.
“If I was in the club’s position, I would certainly buy him.”
Sane, who arrived at the Etihad from Schalke in August 2016, provided 10 goals and 11 assists in the Premier League during the 2018/19 campaign to help City defend their title.
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