The 24-year-old has less than 12 months remaining on his contract, and is currently in talks to potentially extend his deal at San Siro.
However, Ilmilanista reports that both Liverpool and United are monitoring the midfielder's situation and will consider a move in January to sign the player permanently or negotiate a pre-contract agreement for him to join for free next summer.
However, the Ivorian's current wage demands are a stumbling block in negotiations at present, as he is demanding around €6.5m (£5.5m) per season for a five-year contract, a figure Milan are not prepared to pay.
Milan may consider the sale of Kessie in January as they will not want to lose another player for free, having seen Italian goalkeeper Gianluigi Donnarumma join Paris Saint-Germain and playmaker Hakan Calhanoglu move to city rivals Inter Milan this summer, with both players leaving the club for free when their contracts expired.
Kessie has made 187 appearances across all competitions for AC Milan since joining the club from Atalanta in 2017, scoring 30 goals and providing 15 assists. body check tags ::