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.
Read more...
QUIZ! Can you name the top 51 Dutch appearance-makers in Premier League history?
FEATURE The rise and fall of Kieran Trippier – and an international career that’s probably over
‘Scoring in a World Cup is like winning the title – can you imagine millions of people celebrating something you did? It’s insane and made me very proud’: Brazil legend explains how much 2002 goal meant to him
'He already had the ability but didn’t use it because he was afraid to shoot – I said, "You’re a player who has to decide games – you have to take risks, mate"': Liverpool star was forced to become confident by team-mates
