Koulibaly has been regularly linked with a move to the Premier League in recent years following a string of impressive performances for Napoli since joining the club in 2014.
Chelsea are understood to be in the market for a new defender due to uncertainty over the futures of club captain Gary Cahill and David Luiz, both of whom have fallen out of favour under Antonio Conte this season.
Conte has generally preferred the trio of Cesar Azpilicueta, Andreas Christensen and Antonio Rudiger in his back three, and Sport Il Mattino reports that the Italian has now identified Koulibaly as an ideal candidate to bolster his options further.
The report goes on to say that Chelsea could be willing to meet the 26-year-old's £65m asking price in a bid to close the gap back to the top of the table next season.
Koulibaly has made 40 appearances for Napoli across all competitions this term, scoring five goals including a last-gasp winner against leaders Juventus last weekend to take his side to within one point of the champions.
Chelsea, meanwhile, are languishing fifth in the Premier League table, five points adrift of the Champions League places.