The Senegal international has remained loyal to Luciano Spalletti's side for the past couple of years despite persistent links with a switch to the Premier League.
Koulibaly will soon enter the final year of his contract with Napoli, though, and some of Europe's top clubs are still being linked with a move for the 31-year-old.
Manchester United and Barcelona are thought to be keeping tabs on Koulibaly, while Chelsea are stepping up their efforts to sign the defender amid their centre-back search.
The Blues are supposedly willing to pay Koulibaly £8.5m per year to make the move to Stamford Bridge, but their lucrative salary offer may ultimately fall on deaf ears.
According to La Repubblica, Koulibaly's priority is to reach an agreement over a new deal with Napoli, and the centre-back wants to end his playing career with the Italian club.
The report adds that Napoli president Aurelio De Laurentiis also wants to extend Koulibaly's stay, but the player has so far been left dissatisfied with his renewal offers.
Talks between Koulibaly's representatives and Napoli have supposedly been ongoing for 'a few weeks', and Juventus have also been alerted to the Africa Cup of Nations winner's potential availability.
Koulibaly's agent Fali Ramadani offered an update on his client's future last month, during which he affirmed that the centre-back was yet to make contact with any foreign club over a summer transfer.
"There are many rumours, and I want to clarify that we are not in talks with any club for Koulibaly," Ramadani told Corriere dello Sport. "We are waiting to meet with Napoli to decide the best solution for both parties."
Napoli forked out just shy of £7m to sign Koulibaly from Genk in the summer of 2017, and the 31-year-old has gone on to amass 14 goals and eight assists in 317 games for the club in all competitions.
Koulibaly has won the Coppa Italia and Supercoppa Italiana during his time in Naples, and his 2021-22 season brought him three goals and three assists from 34 appearances in all tournaments.
Chelsea manager Thomas Tuchel is set for a defensive shake-up this summer, with Barcelona-bound Andreas Christensen and Real Madrid new boy Antonio Rudiger both departing on free transfers.
Cesar Azpilicueta could also leave before the window shuts amid links with La Blaugrana, but Thiago Silva has committed himself to the club for at least one more season.
Sevilla's Jules Kounde and Inter Milan's Milan Skriniar are thought to be two of Tuchel's top targets, and the Blues are also said to be considering a move for Manchester City's Nathan Ake.