Donnarumma has been a mainstay in Milan's starting XI since making his debut in October last year, with the 17-year-old goalkeeper now seen as the heir to Gianluigi Buffon's throne in the Italy team.
The shot-stopper's exploits, again highlighted in Milan's stunning 1-0 victory over Serie A champion Juventus on Monday (AEDT), has no doubt captured the interest of Europe's biggest clubs but Galliani is confident of keeping Donnarumma.
Asked if he sees Donnarumma as Buffon's replacement, not only in the national team but Juve, Galliani responded via Mediaset program Tiki Taka: "You must be joking. Donnarumma is a Milan player.
"I hope and I'm convinced that he'll be a Milan player for many years to come.
"I think he'll be the heir to Buffon in the national team, though Buffon is still a great goalkeeper. Buffon has a contract with Juventus until 2018, he is doing very well."
Donnarumma has kept four clean sheets this season to help Milan up to third in the Serie A standings, only adrift of second-placed Roma on goal difference, and two behind Juve after nine rounds.