The 25-year-old attempted to impress new manager Frank Lampard in pre-season but he failed to make the required impact to return to the Blues first team.
If Monaco pay the €42m fee at the end of the season, it would make Bakayoko their third most expensive signing of all-time, after just Radamel Falcao and James Rodriguez.
The Provincial club see the return of the powerful midfielder who broke through at the club and played 84 times. He played a major role in Monaco's Champions League run of 2016-17 that led to the Blues paying £40m ($49m) to sign him that summer.
However, he has quickly been deemed surplus to requirements by yet another manager after struggling under Antonio Conte and being loaned out to AC Milan under Maurizio Sarri.
Bakayoko has played just 43 times for Chelsea and Kenedy could be the next first-team star to exit the club ahead of the European transfer window closure on 2 September.
Galatasaray were dismissed by Chelsea who are keen to see their asset regain his form on loan, and therefore increase his transfer value.
After Chelsea's 2-2 draw with Sheffield United where 18-year-old Billy Gilmour debuted due to injury issues, Lampard spoke about why he let go of Bakayoko and Drinkwater in the circumstance.
“Danny has been here for two years and hadn’t played many games. He was eager for his own benefit, which I felt was good for us," Lampard said at Stamford Bridge.
"Bakayoko similarly was here for one season, went on loan and going on loan again to try to bring himself back to where he wants to be.
“If you want to talk midfield players we have got Jorginho, [Mateo ] Kovacic, [N’Golo] Kante, [Mason] Mount, [Ross] Barkley, Reece James coming back from injury who can play in midfield, Andreas Christensen who can play in midfield. I have to make decisions on the squad as a whole, that is my job.”
Monaco are currently in 19th place after a poor start to the season where they have lost two of their first three games, drawing the other one.