The Poland international has been a crucial part of the Bundesliga giants since his controversial move from Borussia Dortmund in 2014.
The 29-year-old has scored 82 league goals for the Bavarians, and he set a record at the weekend for most Bundesliga goals scored by a player in 100 appearances for one club.
Despite this, Lewandowski is concerned about the club's ambition and as a result is considering leaving the Allianz Arena when the transfer window reopens in January.
According to The Mirror, City would have the edge if a bidding war were to ensue due to Pep Guardiola's relationship with the striker, having coached him for two years at Bayern.
Chelsea and Manchester United have previously been linked to the prolific hitman.