Earlier on Tuesday, reports emerged that the Senegal international was ready to sign a three-year contract at Stamford Bridge.
Furthermore, it was claimed that the two clubs were nearing an agreement over a fee which is believed to be in the region of €40m (£33.91m).
The alleged development is in sharp contrast to what was suggested by director Cristian Giantuli in recent days as Napoli fight to retain the services of their long-serving centre-back.
Giantuli said: "Koulibaly is key player for us. There's no bid from any club. We've offered him new deal for €6m net salary per season plus a future role as part of the board.
"It's a huge proposal, €60m gross for Napoli - Koulibaly deserves it all. We didn't need to tell Koulibaly that we're not selling him to Juventus - because we consider Koulibaly untouchable and non-transferrable."
While there has been nothing official from either Chelsea or Napoli, Koulibaly has now commented on the latest developments regarding his future.
In response to being quizzed on the link with Chelsea, the 31-year-old is quoted by journalist Romain Collet-Gaudin as saying: "I'll confirm that later, but it's on the right track."
Although a transfer is still not regarded as a foregone conclusion, it appears that Chelsea are well on their way to making multiple signings in the space of a few days.
Chelsea are said to be on the brink of signing Manchester City winger Raheem Sterling, who has allegedly undergone a medical ahead of a switch to Stamford Bridge.
The West Londoners are also attempting to seal a deal for Sterling's City teammate Nathan Ake, a player who began his professional career at Stamford Bridge.
While Ake would arrive as a direct replacement for Antonio Rudiger on the left-hand side of a back three, Koulibaly would replace the leadership qualities of the outgoing Germany international.
Koulibaly also has compatriots and former teammates at Chelsea, the player having recently won the Africa Cup of Nations with Senegal alongside goalkeeper Edouard Mendy.
Blues midfielder Jorginho was in Naples during the early stages of Koulibaly's stint with the Serie A giants before moving to the Premier League in 2018.