Donnarumma has been heavily backed to join Manchester United at the end of the season.
Real Madrid continue to monitor David De Gea, leading to United's interest in the 17-year-old.
Madrid themselves have been linked with a move for Donnarumma if their bid to sign De Gea fails.
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Gianluigi Donnarumma could end up staying at AC Milan
David De Gea continues to be linked with a move away from Manchester United
But Milan boss Montella reckons his star asset will sign a new deal after his 18th birthday on February 25.
"We have to wait for him to reach 18 years old then I think Milan will renew his deal," Montella said.
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"He loves Milan and I am so happy to have him."
Real Madrid are on the lookout for replacements for Keylor Navas
Donnarumma has enjoyed a fine season, helping Milan up to seventh in the Serie A table.
The youngster also made history by becoming Italy's youngest-ever goalkeeper in September, replacing Juventus stalwart Gianluigi Buffon.