The winger had an indifferent season at club level with Premier League champions City, scoring a respectable 10 goals and making 10 assists, but only starting 21 matches, six fewer than the 2017-18 campaign.
Sane subsequently emerged as a primary target for Bayern, whose rebuild job will continue in the close-season after the departures of long-serving duo Franck Ribery and Arjen Robben.
Bayern president Uli Hoeness confirmed the club's interest last month and CEO Karl-Heinz Rummenigge said they are ready to open talks over a summer move, saying: "We'll try it. But I can't promise whether it will be a success".
Since then, however, Hoeness has bemoaned City's "insane" valuation of the winger and Goal reported recently that the Premier League champions are trying to convince him to extend his contract, with two years to go on his current one.
But Sane failed to commit to Pep Guardiola's side post-match when asked about the Bayern speculation.
He told reporters: "I'm going on holiday now. Everything else will be seen. That's it with the questions about Bayern Munich."
While Sane has remained quiet on the rumours surrounding his future, his Germany team-mates have been happy to discuss it.
Bayern Munich duo Serge Gnabry and Joshua Kimmich have said they would be happy to see Sane turn up at the Bavarian club, but his City co-star Ilkay Gundogan does not expect him to leave England just yet.
Meanwhile, Julian Draxler says he is unsure what his fellow ex-Schalke star will decide, but admitted that the players have been teasing Sane about the speculation.
On the other hand, former Germany and Bayern hero Lothar Matthaus is convinced that a move is on the cards, as he wrote in a column last month: "A player who, in my eyes, will enchant the Bayern fans next year is Leroy Sane. I am sure he will move to Munich."