The deal includes the option for the Serie A side to purchase the 23-year-old permanently for £35.56 million, according to Sky in Italy (h/t Sky Sports).
Bakayoko will have a medical Monday before completing his move to the San Siro, per the report.
The midfielder only arrived at Chelsea last summer from Monaco after playing a key role in helping the Ligue 1 side win the French title.
However, he has struggled to live up to his £40 million price tag at Stamford Bridge and found it tough adapting to the Premier League.
His chances of regular football this season look even slimmer after Chelsea moved to strengthen their midfield. Jorginho has arrived from Napoli and Mateo Kovacic from Real Madrid.
The Blues also have Ross Barkley, Danny Drinkwater and Cesc Fabregas in the squad, which means competition for places is fierce.
Bakayoko did feature in pre-season but did not look too impressive, according to Mark Worrall at ESPN FC:
The Premier League transfer window has closed, but it remains open throughout Europe, and the Blues can still sell and loan players.
New manager Maurizio Sarri has said Bakayoko is one player who could leave, per ESPN FC's Liam Twomey:
Chelsea have already agreed to loan out fringe players such as Kurt Zouma and Michy Batshuayi as they trim their squad.
Bakayoko looks to be next on the list. A departure from Stamford Bridge looks a good option for a player who is still only 23 but seems to have lost his way in London.
Football analyst Matteo Bonetti explained how he might be used at AC Milan:
At his best, Bakayoko is a dynamic and aggressive midfielder capable of taking control of matches. He will be hoping a move to AC Milan can help him rediscover the form he showed at Monaco and get his career back on track.