The 27-year-old, who was at Milan on loan in 2018/2019, will spend two seasons on loan at the Italian club again.
According to Sky Sports, Bakayoko is having a medical before he signs his contract.
Bakayoko has only managed 43 appearances for Chelsea since signing in 2017, spending much of that time on loan at various clubs.
He will be hoping to get some stability in his career at Milan, who have a purchase option within the loan agreement.
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