The Rossoneri have been in discussions for several months with Kessie over signing a new deal at the San Siro, with his current contract set to end in the summer of 2022.
With uncertainty surrounding his long-term future at the club, Kessie has been linked with a move away from AC Milan and Premier League giants Tottenham and Arsenal are claimed to be potential destinations for him.
But the Milan outfit see the midfielder playing a huge role at the club going forward and are trying to extend his contract until the summer of 2026.
However, according to Italian daily Gazzetta dello Sport, Kessie is yet to agree to the terms proposed by AC Milan.
The player is open to staying but is not satisfied with the €3m per year offer made by the Italian giants.
Kessie wants to see AC Milan return to the table with a better proposal.
The 24-year-old’s suitors may be encouraged by AC Milan’s inability to agree a new contract with Kessie so far.