Bakayoko joined Chelsea from Monaco in last summer's transfer window, and made over 40 appearances during his first season in English football.
The France international struggled for consistency, however, and has been strongly linked with a move away from Stamford Bridge this summer.
Bakayoko was not involved in Chelsea's Premier League clash with Huddersfield Town on Saturday, with the midfielder believed to be on the verge of sealing an exit.
According to Goal.com, Milan have won the race to sign the 23-year-old, who will join the Italian giants on a season-long loan with the view to a £31m permanent move at the end of the 2018-19 campaign.
Bakayoko played 92 times for Monaco ahead of his move to Chelsea last July.