Despite frequent links with a switch to the Premier League over the past couple of years, the 31-year-old has remained faithful to the Partenopei and will soon celebrate his eight-year anniversary in Naples.
However, Koulibaly now has just 12 months left to run on his contract with Luciano Spalletti's side, who are running the risk of losing him on a free transfer at the end of next season.
Manchester United were persistently linked with a move for Koulibaly last year, but new manager Erik ten Hag is seemingly focusing on other centre-back targets for the current window.
Chelsea and Barcelona are now said to be the two frontrunners for the Senegal international's signature, and the Blues have apparently stolen a march on the Blaugrana in the race for his signature.
According to The Mirror, Koulibaly is a name that has been mentioned at Stamford Bridge, and the former Metz and Genk defender would be keen on a move to the English capital.
In spite of Koulibaly's contract situation, the report adds that Napoli are still prepared to demand a fee of £40m to sanction his exit, and Chelsea are willing to offer the centre-back an £8.5m-a-year deal.
Previous reports had claimed that Koulibaly could picture himself ending his playing career at Napoli, where he has amassed 14 goals and eight assists from 317 appearances in all competitions.
The Africa Cup of Nations winner registered three goals and three assists in 27 Serie A outings for the Partenopei last season, helping his side seal Champions League qualification with a third-placed finish.
Koulibaly has won the Coppa Italia and Supercoppa Italiana during his time in Naples, and he could form a part of a new-look Chelsea backline in 2022-23.
Thomas Tuchel has already lost two defensive mainstays on free transfers, with Antonio Rudiger joining Real Madrid while Andreas Christensen closes in on a switch to Barcelona.
Cesar Azpilicueta could also leave before the window shuts, while Thiago Silva's contract extension only takes the 37-year-old up to the end of next season.
Juventus centre-back Matthijs de Ligt is still said to be Tuchel's top target, but the Old Lady are demanding a mammoth £102m to part ways with the 22-year-old.
Furthermore, Inter Milan have supposedly slapped a £55m valuation on the head of Milan Skriniar amid interest from Paris Saint-Germain, leading Chelsea to consider Koulibaly as a cheaper alternative.
The Blues have not made any major incomings yet this summer, but a double swoop for Leeds United's Raphinha and Manchester City's Raheem Sterling is understood to be progressing well.
Chelsea also confirmed the exit of Romelu Lukaku on loan to Inter Milan on Wednesday, as the 29-year-old returns to San Siro a year after his £97.5m transfer to Stamford Bridge.