The Ivory Coast international remains a key man at San Siro, contributing five goals from 21 appearances in all competitions during the current campaign.
However, the 25-year-old is still to extend his contract past the end of the season, a pressing concern for both player and club.
According to Calciomercato, Kessie is happy to pen fresh terms at Milan, providing that they are willing to meet his wage demands.
As it stands, however, that is said to remain uncertain, with the report claiming that Spurs are the frontrunners for the player's signature.
Paris Saint-Germain are also regarded as a potential destination for Kessie, who has been representing Milan since 2017. body check tags ::