The Red Devils stopper has been linked with a move to the Bernabeu for years.
De Gea was on the brink of making a switch to Real in 2015 but for an error over the paperwork scuppering the deal.
The Sun now claim Jose Mourinho is willing to let the Spaniard leave should he find a replacement.
Donnarumma has just signed a new contract at Milan but should the Serie A outfit fail to qualify for the Champions League he will re-evaluate his future.
Milan have spent big this summer as they look to return to their glory years.
Romelu Lukaku (v West Ham, 2017)
De Gea wants to move to Real but will not force a switch to the Bernabeu with his contract expiring in 2019.
The top four in Serie A this season will automatically qualify for the Champions League next season.
And Milan know should they fail to make it, one of their prized assets in Donnarumma will likely leave.
United return to Premier League action tomorrow lunchtime when they travel to Swansea.
De Gea will be looking for back-to-back clean sheets following the 4-0 win over West Ham at Old Trafford last weekend.