The Germany international has been heavily linked with the Bundesliga champions in recent weeks.
Sane fell down the pecking order at the Etihad Stadium last season, making only 21 starts in the Premier League.
That led to questions over the winger’s future, with Bayern making him one of their leading transfer targets.
However, the £90m-rated Sane has decided to extend his contract at City rather than returning to Germany.
The Premier League champions are hopeful of making a breakthrough in talks over a new deal, with Sane’s current contract set to expire in 2021.
READ MORE
Jadon Sancho: Where next for England’s once-in-a-generation star?
Fernando Torres: How Rafa Benitez pushed me to become one of the best strikers in the world
