The Bavarians are keen to add to their ranks ahead of the new season, and have now supposedly set their sights on the Netherlands international, who would replace Mark van Bommel
The Bundesliga giants are looking to add another midfielder to their squad and have previously been linked with players such as Javi Martinez and Lars Bender.
However, they have now turned their attention to De Jong instead as they seek a cheaper alternative.
The 27-year-old joined City from Hamburg in January 2009 and quickly became an important member of Roberto Mancini's squad.
However, he lost his starting berth last season as the Citizens won the Premier League, and City appear to be ready to cash in on the Dutchman this summer if a good offer comes in.
De Jong's current contract with the Manchester side is due to expire at the end of the 2012-13 campaign, and an offer in the region of €10 million could be enough to lure him away from City.