The 32-year-old has established himself as one of City’s best-ever midfielders since joining the club from Borussia Dortmund in 2016.
He has scored 51 goals and registered 34 assists from 268 appearances for the Citizens.
However, earlier this year, it was claimed that the Germany international may be allowed to depart the Etihad with his current contract due to expire in 2023.
He instead remained with the Premier League champions, going on to make 11 starts and three substitute outings this campaign.
According to 90min, Bayern Munich are keeping close tabs on the player’s situation ahead of attempting to sign him on a free transfer.
The report claims that the German playmaker is tempted by the prospect of another stint in the Bundesliga.
The Bavarians are already well stocked for midfielders with Joshua Kimmich, Leon Goretzka, Ryan Gravenberch and Marcel Sabitzer all fighting for regular sports in that area of the pitch.