Donnarumma – out of contract in 2018 – has been linked with Spanish and European champions Madrid after announcing that he will not sign a Milan renewal.
However, the 18-year-old Italy international could still extend his contract at San Siro following the European Under-21 Championship.
Asked about Donnarumma ahead of Spain's U21 showdown with Italy on Tuesday, Asensio said: "He is a young goalkeeper, who has shown that he is a great keeper.
"He has a great future, but he also has a great present.
"If he is prepared or not to play in Real Madrid, I do not decide it."
Donnarumma has been Milan's undisputed number one since making his debut as a 16-year-old.
Seen as the heir apparent to Gianluigi Buffon in the Italy team, Donnarumma appeared in all 38 Serie A matches as Milan finished sixth last season.