The defensive midfielder failed to impress at the Blues under Antonio Conte a few years ago, and has been on loan ever since.
Bakayoko was at Milan for some time, while he was at Monaco last term.
Neither club wants to buy him permanently at the current asking price.
Now Chelsea are hoping to strike a deal for £20 million with Milan.
The Sun claims the club simply want to get the player's wages off the wage bill for the coming two years.