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.
Monaco 
Stade Brestois 29 
Bordeaux 
Nimes 
Bayern Munich 
FC Augsburg 
Paris Saint Germain 
Toulouse 
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen