The 27-year-old has a year left on his contract and has no future at Chelsea after spending several years away from the club on loan.
AC Milan are pushing to land him and they worked out an agreement over a contract with his agents in Italy on Thursday.
The Rossoneri are now trying to reach an agreement with Chelsea but the Frenchman has other offers on his table as well.
According to Italian broadcaster Sportitalia, four other clubs from Turkey and France have made proposals to the midfielder this summer.
But Bakayoko is clear about his intention to join AC Milan, where he had a season on loan in the 2019/20 campaign.
He loved his time in Milan and also had another loan spell in Italy at Napoli in the 2020/21 season as well.
The Frenchman is pushing for a move to AC Milan and has told his representatives and Chelsea to get the deal over the line.
The Rossoneri are now trying to work out the details of the switch with Chelsea as they push to sign Bakayoko.
