Bakayoko will have a medical this week and if all goes well, he may travel with the rest of Chelsea squad to China and Singapore next Monday.
Negotiations are continuing about the value of the deal and the transfer fee is likely to be between £35m and £40m.
Bakayoko, 22, helped Monaco win the French title last season for the first time in 17 years.
His arrival is likely to pave the way for Nemanja Matic to leave.

Manchester United want Matic but Chelsea are understood to be reluctant to sell him to United after they secured the signing of Romelu Lukaku.
