The report claims that manager Antonio Conte has placed a £53million bid on the table for the 25-year-old centre-back.
However, it also reports that the Serie A side have rejected the offer and are not willing to sell the defender as the club are planning to mount a serious title challenge next season.
This comes after Tuttosport reported that Italian giants Juventus rejected a £52million offer for full-back Alex Sandro from Chelsea.
Napoli have enjoyed two consecutive top three finishes in the league but they have been unable to pose a genuine threat to Serie A champions Juventus, who have clinched the title for the last six campaigns.
The team from Naples have not won the league title since the 1989-90 season when Argentinian legend Diego Maradona was the country’s most outstanding performer.
Koulibaly has been an integral part of the Napoli team since joining in the 2014 summer transfer window from Belgian side Genk.
The Senegalese defender was instrumental for Napoli last season, making a total of 38 appearances in all competitions and scoring two goals.
The defender’s contract with the Serie A side expires in the summer of 2021.