The Serie A side won the race for the midfielder’s signature in the transfer window and took him to Italy on a season-long loan deal.
Napoli have handed Bakayoko four appearances in Serie A and two in the Europa League so far, but they have already seen enough to know they want him on the books permanently.
And, according to Italian daily Corriere dello Sport, Napoli have started talks with Chelsea to sign Bakayoko permanently.
Bakayoko is surplus to requirements at Stamford Bridge and Napoli will hope to be able to reach an agreement with Chelsea to end the player’s association with the Blues.
The former Monaco midfielder is happy at Napoli and is keen to make sure he stays at the club.
Bakayoko, 26, has made a total of 43 appearances for Chelsea, but may depart Stamford Bridge without ever adding to that number.
Napoli have enjoyed a strong start to the new Serie A season and sit in third place with 14 points, just three points off early leaders AC Milan.
