The midfielder is set to be unveiled as a new addition to Antonio Conte's side as they bring an end to a transfer saga which became protracted due to concerns regarding the player's fitness.
Chelsea are confident the 22-year-old can complete a medical despite recent surgery on a knee injury that requires ongoing treatment.
The Blues' medical staff are confident he will recover from the injury, and the midfielder is clearly excited about working with his new team-mates.
After provoking a reaction from Manchester United fans earlier in the day, Bakayoko posted an image on his Instagram Stories from Chelsea's training ground, decorating it with arrows with "soon" written below them pointing to the field.
Bakayoko will become Chelsea's second signing of the summer, following the £35m capture of Antonio Rudiger from Roma.
Conte has seen John Terry, Nathan Ake and Asmir Begovic leave so far in the transfer window, and Diego Costa is expected to follow as he was granted leave from training to negotiate a move to Atletico Madrid.
Nemanja Matic is also expected to leave as a result of Bakayoko's arrival, with United and Inter possible destinations.