The 18-year-old's agent Mino Raiola has held talks with officials in Milan but the two parties have failed to come to an agreement over a new deal and he now looks set to be allowed to leave this summer.
His current deal runs until 2018 but Milan are keen for him not to run out of contract and therefore leave in on a free transfer in a year so he will be sold this summer.
In a statement, AC Milan CEO Marco Fassone said: “Raiola informed us that Donnarumma has made a definitive decision not to renew the contract with Milan.
“We had made a strong proposal. The player evaluated it and made some evaluations that were not just economic, but he told us that he does not wish to renew the contract and his time with Milan will therefore conclude by June 30, 2018.
“We were taken by surprise, as we had hoped Donnarumma would be the goalkeeper taking Milan into the future. Naturally, the decision leaves a bitter taste in the mouth, but now we have to go forward.”
Manchester United have been linked with a move for the stopper if they were to sell star man David de Gea to Real Madrid but the Champions League holders are also thought to be pondering a move as the transfer merry-go-round gets into full swing.