Donnarumma has been linked with a move away from San Siro, with Paris Saint-Germain among the club's reportedly interested in the shot-stopper.
The 20-year-old has not always had the best relationship with supporters, with the youngster having once been reduced to tears by a banner produced by the home support, who were upset with the talented goalkeeper over a contract dispute.
But Boban has suggested the Italy international will be staying in Milan, although he accepted that the situation could change should the player decide he wants to leave.
"[Paolo] Maldini said that we are happy to have probably the best goalkeeper in the world, surely the best talent in the world in that role," Boban told CalcioMercato on Tuesday.
"For the moment, he remains. He can change, but it is not said that he will leave."
Donnarumma joined Milan as a 14-year-old in 2013 and has already made 164 first-team appearances.
He will be playing for a new manager this season in the form of Marco Giampaolo.
And Boban thinks the new boss was the right choice to lead the club back to the top of European football.
"He is one of the few coaches that makes you clearly understand how he wants to play, in every situation," he said.
He continued: “Giampaolo will find the right path, with the players but also with the game."
They will be hoping to go one better in new season, while also looking to close the substantial gap on champions Juventus, who finished 22 points clear of them.
Despite that fifth-place finish the club are facing a season without European play, having been banned from the Europa League following FFP violations.