The midfielder has reached an impasse in contract negotiations with the club, as per Gazzetta dello Sport.
The Ivorian is reportedly asking for a ‘special bonus’ after a great season with the Rossoneri.
With 11 months left on his contract, his future is anything but certain at the club.
Kessie currently earns €2.2 million per year net, a figure he expects to reach €6m.
However, Milan are not willing to exceed €4m.
The club wants to keep the midfielder next season and remain tight-lipped about the current situation.
Talks are ongoing, and Paolo Maldini is trying to avoid another Gianluigi Donnarumma-like situation.
The priority of the Rossoneri is to make Kessie the leader of the midfield and perhaps the future captain of the club.
Liverpool are considered possible suitors, with manager Jurgen Klopp keen to bring the Ivorian to Anfield.
Jordan Henderson’s future at Liverpool is unclear, with the Reds captain entering the final two years of his contract.
Georgino Wijnaldum’s exit to Paris Saint-Germain, coupled with the uncertainty around Henderson’s contract, means Liverpool desperately need a top-quality box-to-box midfielder.
Kessié would be the perfect partner to Fabinho and Thiago.
Whether it is breaking the lines, acting as a defensive presence, bombing forward, or intelligently using his physical attributes to progress the ball, Kessie is vital to the way Milan play.
In the decisive late game of the season with top-four qualification hanging in the balance, Kessie converted two penalties.
It takes immense bravery and courage to have the hopes of a whole fanbase on your back.
It remains to be seen whether Milan’s beloved ‘El Presidente’ will stay with the Italian Giants amid high interest from Liverpool.