The Serie A giants were unwilling to match the contract demands proposed by the 21-year-old's agent Mino Raiola and so he is set to depart the San Siro after spending his entire career with the club.
Milan have wasted no time to find a replacement, after they announced on Thursday the arrival of Lille stopper Mike Maignan on a five-year deal.
The Daily Express reports that both Chelsea and Spurs have since been alerted about Donnarumma's availability and will now consider approaching the player this summer.
Even though Tottenham have yet to appoint a new manager, the club are believed to be looking for a long-term replacement for captain Hugo Lloris, who turns 35 in December.
Meanwhile, Blues boss Thomas Tuchel is set to offload Spanish goalkeeper Kepa Arrizabalaga this summer and will therefore be seeking a replacement.
Donnarumma, who has also been linked with a move to Juventus, made 251 appearances for Milan since his debut as a 16-year-old in 2015, keeping 75 clean sheets.