The French midfielder cost Chelsea £40million when he signed from Monaco in 2017 but he has struggled at Stamford Bridge and has been told he can leave.
Bakayoko made 42 appearances for AC Milan during a loan spell in 2018/19 and then last season was on loan at Monaco.
The 25-year-old has two years left on his £100,000-a-week Chelsea contract and the Blues would be willing to sell him permanently to help fund their summer transfer plans.
But AC Milan are keen on a loan with an option to make the deal permanent next summer.
Bakayoko made 42 appearances under Antonio Conte in his first season at Chelsea despite struggling following his move to England. Maurizio Sarri made it clear he was not part of his plans and he has been told he has no future at Chelsea under Frank Lampard.