Donnarumma became the youngest goalkeeper ever to debut in Serie A at the age of 16, and has since become Milan's undisputed number one despite only turning 18 last month.
The teenager, who stands at 6'5", also became Italy's youngest-ever stopper when he made his international debut in last September's friendly with France.
Juventus and Manchester United have both been linked with a move for the youngster, but Donnarumma, whose current deal expires in June 2018, has revealed that he wants to pen fresh terms at San Siro.
"I hope to stay at Milan," Donnarumma told Sport Mediaset. "I want to stay because I am a Milan fan. My contract is something my agent will deal with."
It has previously been claimed that Donnarumma, despite still being a teenager, could earn upwards of £80,000 per week if he signs on the dotted line with Milan.