The 29-year-old joined Bayern in 2014 from German rivals Borussia Dortmund and he made his 100th appearance for the club over the weekend.
Lewandowski netted twice on Saturday against Mainz to take his tally to 82 league goals and set a record for the most Bundesliga goals scored by a player in 100 appearances for one club.
However, reports claim that the Poland international has grown frustrated by a lack of movement in the transfer market by Bayern and he is fearful they will be left behind by their European rivals.
It’s understood that he will attempt to force through a move in January and City boss Pep Guardiola is keen to secure a reunion.
The likes of Chelsea, Manchester United and Real Madrid have all previously been linked with his services and it’s expected that City will need to fend off plenty of competition to win the race.