The former Borussia Dortmund has just completed his second season at the Nou Camp.
But BILD says Dembele could be on his way back to the Bundesliga, where Bayern are keen.
The German giants see Dembele as an alternative to Leroy Sane. If a deal with Manchester City cannot be settled over Sane, Bayern will move for the France international.
Bayern need a new winger signing after the departures of veteran pair Arjen Robben and Franck Ribery.