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 in February.
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 according to Mirabelli, Donnarumma wants to stay with his current club.
"We have had talks over the past week with his agents, which is normal," Mirabelli is quoted as saying by talkSPORT. "We also had talks with Gigio and we asked him if he wanted to stay at Milan.
"He responded in an affirmative matter that he is happy here and he wants to keep playing for Milan. It is now up to us to find an agreement with his agents."
Donnarumma came through the youth system at Milan.