Napoli club president Aurelio De Laurentiis was instrumental in keeping Koulibaly at the Stadio San Paolo this season, despite repeated moves from Chelsea last summer, but the defender could use a lack of Champions League football to push through the transfer he wanted last year.
The Senegal international renewed his contract in September until 2021 after an initial dispute with Napoli, however, his new deal doesn't include a release clause, with Chelsea having bid close to £50 million in August.
Napoli, who lost 3-1 to Real Madrid in the first leg of their Champions League last-16 encounter, are currently third in Serie A, but have Atalanta, Lazio and both Milan clubs in hot pursuit. Only three Italian clubs will qualify for next season's Champions League.
Internazionale are also thought to be interested in signing Koulibaly, but have a six-point gap to make up on Napoli. The Italian giants are targeting a major defensive signing and have increased their spending power after the arrival of the Suning Holdings Group, who now hold a controlling stake in the club.
Chelsea have improved their options in central defence since last summer's bids for Koulibaly, having re-signed David Luiz in a £32 million deal from Paris Saint-Germain and having recalled Nathan Ake from his loan move at Bournemouth.
They are also expected to bring back Andreas Christensen from his two-year loan deal at Borussia Monchengladbach, but Chelsea may find room for Koulibaly as Conte has a strong professional admiration for the 25-year-old.
Napoli appear to have readymade replacements in their squad having signed Nikola Maksimović from Torino last August, while they also have Lorenzo Tonelli and Raul Albiol on their books.