Bakayoko’s scheduled medical has been delayed until this week because he had minor knee surgery at the end of last season.
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.
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