With Real seemingly desperate for a new number one and Jose Mourinho insistent that David de Gea will not be leaving Manchester United, it puts Chelsea in danger of losing the Belgian.
But the reigning Premier League champions could secure a readymade replacement in the shape of Donnarumma if speculation emerging from Italian outlet Corriere dello Sport is to be believed.
Donnarumma has been Milan's starting goalkeeper since the age of 17 and is widely tipped for superstardom in the coming years. But that is unlikely to come with the Rossoneri, with super-agent Mino Raiola apparently keen for his client to move on.
Speaking earlier this month, Raiola publicly urged the young Italian to quit Milan. Similarly, it was believed that the agent was the one behind Donnarumma's temporary refusal to sign a new contract at San Siro last summer. A u-turn soon followed, but Raiola hasn't given up.
"Gigio has made a choice, to stay at Milan, and I respect that," he said recently.
"But if he were to ask me to arrange a transfer, I would immediately go to work because there are important requests. [In my opinion], he should leave Milan."
Donnarumma has also been a rumoured target for Real, particularly last summer.