The 24-year-old's future remains the subject of much speculation, as his contract at San Siro is due to expire next June, and there are currently no signs that he will be penning fresh terms.
According to Corriere dello Sport, there is also strong interest from Real Madrid, who believe that he could be a long-term replacement for Casemiro.
The report claims that Milan have now given up on a contract renewal, meaning that the Italian giants could attempt to sell him during the January transfer window.
Kessie has scored 32 goals and registered 15 assists in 196 appearances for I Rossoneri since making the move from Atalanta BC.
This term, the midfielder has again been a key player at San Siro despite the speculation surrounding his future, scoring twice in 12 appearances in all competitions. body check tags ::