The 18-year-old goalkeeper is regarded as one of the biggest talents in the game and has been linked with a move away from San Siro on numerous occasions.
Juventus reportedly sees the Italy international as the long-term replacement for Gianluigi Buffon, while a number of Premier League clubs have also been credited with an interest in Donnarumma.
But the shot-stopper has made it clear a transfer is not on his mind at this stage in his career.
"I hope to stay at Milan," Donnarumma said.
"I want to stay because I am a Milan fan."
The youngster's contract is due to expire in 2018 and there has not yet been an agreement in talks over a new deal.
Donnarumma sees no reason for concern just yet, though, and will let his agent Mino Raiola handle the matter.
"My contract is something my agent will deal with," he said.