AC Milan have announced that Gianluigi Donnarumma has rejected their offer of a new contract and does not intend to extend his current deal, which expires in 2018.
The news was confirmed by the club's chief executive, Marco Fassone, at a press conference arranged after talks on Thursday.
Fassone said that he had been informed by Donnarumma's agent, Mino Raiola, that the young goalkeeper's decision to leave the club upon the expiry of his current terms was "final".
Milan will now have to decide whether to cash in on the 18-year-old, who is widely regarded as the brightest goalkeeping prospect in world football, or allow his contract to run down and receive what is likely to be significantly smaller fee through a tribunal.
"Mino Raiola has informed me of Donnarumma's decision not to renew his contract with AC Milan," Fassone said. "It's a final decision taken by the player.
"I remember that 10 days ago we made an important offer to the player - even more important that what the newspapers have written. The player made his technical, economical and personal considerations and has decided to reject it.
"He will end his relationship with AC Milan on June 30, 2018."
Donnarumma became the second-youngest goalkeeper to play in Serie A when he made his Milan debut as a 16-year-old in 2015.
He has since cemented his position as the club's No. 1 stopper and became the youngest goalkeeper to play for Italy at 17 years and 189 days last year.
Madrid themselves have also been credited with interest in the man regarded as Gianluigi Buffon's long-term successor as they seek an upgrade on current first-choice Keylor Navas.
Goal reported on Thursday morning that Donnarumma was set for a decisive day of talks involving Raiola and Milan negotiator Massimiliano Mirabelli.
The Rossoneri were ready to pay the teenager €4.5 million per year before bonuses and willing to insert a release clause into the deal, but have been unable to persuade him to sign.