Reports in Italy claim that the youngster has told agent Mino Raiola to try to get him out of the new contract he signed at the San Siro during the summer.
The 18-year-old was heavily linked with a move away from the club during pre-season, with his contract having been due to expire next June. However, after much wrangling, the shot-stopper eventually agreed terms on a new four-year deal.
Italian publication 'La Gazzetta dello Sport' now claims that Donnarumma, who even received death threats when it was thought he was going to leave, felt pressured into the contract by the AC Milan hierarchy and is thus attempting to have the deal annulled.
European heavyweights Real Madrid and PSG are both huge admirers of the Italy international's abilities and the pair could be set to swoop in January.
Should Raiola succeed in his quest, Donnarumma's previous contract would be reinstated, leaving him with just six months left on his deal.
AC had been expected to return to their best this season after a summer spending spree, but a series of indifferent performances led to the sacking of Vincenzo Montella, with the club languishing in seventh place in Serie A.
Donnarumma has started all 16 of AC's Serie A games so far this season and is expected to be Italy's new No. 1 following Gianluigi Buffon retired in the wake of Italy's failure to reach the World Cup.