Donnarumma has established himself as the Rossoneri's No.1 since making his first-team debut as a 16-year-old in October, 2015 and the San Siro side had hoped that he would commit his future to the club when he turned 18 on February 25.
However, the two parties have yet to reach an agreement, with the shot-stopper's agent, Mino Raiola, reportedly demanding between €4.5 million and €5 million per year for his client, which is almost double what Milan are offering.
Raiola is also reluctant to let Donnarumma commit his future to a club that is in the middle of a protracted takeover that was meant to be completed on March 3, with CEO Adriano Galliani also unable to agree any major deals given the Chinese Sino-Europe Group (SEG) has yet to fulfil certain financial demands.
Indeed, he has already previously stated that whether the Italy international stays on at the San Siro hinges upon the prospective new owners' transfer plans.
"I think it is only right for me to see what Milan will be like," Raiola stated. "Until I see the new ownership and I begin to talk to them, I cannot have a clear idea [on Donnarumma's future].
"Does he deserve a great Milan? No, he deserves a great team. I'm not married to anyone. My job is not to be a fan of a team."
The current impasse has alerted the attention of Europe's top clubs, including Juventus, who are looking for a replacement for the 39-year-old Buffon.
Goal understands that the Bianconeri are closely following the situation at Milan with great interest, as they believe Donnarumma is their current captain's natural heir.
Furthermore, Juve are also hoping to take advantage of the uncertainty at the Rossoneri by making a summer move for Mattia De Sciglio, who, like Donnarumma, only has just over 12 months left on his present Milan deal.
While it has yet to be confirmed that Bianconeri boss Massimiliano Allegri will see out the final year of his contract in Turin, particularly amid intense speculation linking him to Arsenal, he is open to staying.
If he does, the former Milan boss would like to be reunited with De Sciglio, whose form has fluctuated in recent years but remains an excellent attacking full-back, as he showed at Euro 2016, and one with the added bonus of being able to play on either flank.
For now, though, Juve are willing to bid their time before deciding to launch what could be a sensational double swoop for two of their Serie A rivals' most prized possessions.