The struggling Bundesliga giants are disappointed with the 26-year-old's return this season and could accept about £30million for a player they wanted £80m for in the summer.
Bayern have reportedly already offered Ribery to Manchester City, Real Madrid and Barcelona, while Manchester United and Chelsea would also be interested for the right price.
Unhappy: Franck Ribery could leave Bayern Munich in the New Year
Ribery seemed keen on a move to Madrid in the summer, but a resolute Bayern board, led by chairman Karl-Heinz Rummenigge and president Franz Beckenbauer, resisted all offers.
Bayern coach: Louis van Gaal
Since then, Ribery has been struggling with a knee injury and has looked poor in his six appearances this season.
His only goal came in a 5-1 win at Borussia Dortmund, a rare highlight in a season that has seen Bayern stuggle in mid-table. They stand eighth of 18 in the League and are unlikely to get through their Champions League group.
Ribery is said to have a poor relationship with coach Louis van Gaal and has shown earlier in his career that he does not play well when unhappy.
The former Metz, Galatasaray and Marseille player has rarely stayed in one place too long, having played for seven teams already in his short career.
His contract ends in June 2011, meaning that, next summer, Bayern will be unable to command the kind of fee they have been looking for.
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