Bakayoko starred for Monaco as they shocked French football to win the Ligue 1 title ahead of Paris Saint Germain.
But despite Monaco's attempts to extend his contract, the France international has refused to sign an extension which has forced the club to consider selling.
And it now appears likely the 22-year-old will follow his former team-mate and new Manchester City midfielder Bernardo Silva in moving to the Premier League.
According to the Independent, Blues boss Antonio Conte views Bakayoko as key to adding more ‘thrust' to his side.
Chelsea target Tiemoue Bakayoko had an excellent season for Monaco
Jose Mourinho signed Nemanja Matic in 2014 when he was Chelsea boss
Conte is said to want six signings this summer to add depth and more strength to his squad as they look to retain the Premier League and mount a challenge in the Champions League.
The report also says Bakayoko's arrival could lead to the departure of Nemanja Matic to Manchester United.
Matic was a regular for Conte alongside N'Golo Kante but the signing of Bakayoko may mean fewer minutes for the Serbian.
Jose Mourinho would like to bring Nemanja Matic to Manchester United
United boss Jose Mourinho signed Matic in 2014 when he was Chelsea boss and remains an admirer of the Serbian international.
It is claimed Matic would like to work with Mourinho again and personal terms have already been discussed between player and club.
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The chance to give Paul Pogba more freedom is also said to be a reason why Mourinho wants the defensive midfielder.