The 18-year-old had another solid season for the Italian giants, starting all 38 games in Serie A.
The goalkeeper has been heavily linked with a move away from the San Siro this campaign.
And according to Transfermarketweb, Milan are keen to agree a deal with Donnarumma and his agent Mino Raiola.
They say Manchester United, Manchester City, Real Madrid and Juventus are all chasing the highly-rated stopper.
Milan have reportedly offered the youngster a bumper pay rise to stay in Italy.
Donnarumma could be a possible replacement for David De Gea at United.
The Spain international has been tipped to quit Old Trafford and join Real in a blockbuster summer move.
De Gea, 26, nearly joined the Spanish giants in 2015 but a late fax stopped the deal.
