Catalan newspaper Mundo Deportivo (h/t Joe Short of the Daily Express) reported it may take a fee of up to £62 million for either club to secure the defender, who has continued his impressive form in Napoli's back line this season.
The Senegal international impressed last term and was linked with a move to Stamford Bridge over the summer, but he stayed in Naples and has helped lead his side to the summit of Serie A, while Barca lead La Liga.
BBC pundit Mina Rzouki recently attributed a great deal of Napoli's success to the dominant form of their central defender, nodding to the old adage that while attack wins games, it's defence that often wins championships:
One major stumbling block for Barcelona, however, is that Koulibaly appears to be content in Italy for the time being and recently praised manager Maurizio Sarri in an interview with Italian daily Il Messaggero (h/t Football Italia):
“He rediscovered me, he gave me confidence. He really is a genius, he sees things others don't see. He makes you understand how football is and isn't unpredictable. He's a scholar.
“Any question you ask him, he always has an answer—and it's always right. He helps you to think as a team and not as an individual.
“When he arrived he told me: 'Do as I say and you'll become an important player.' I'm trying, but I know I can still improve."
While Napoli boast a perfect record in Serie A, a 2-1 defeat at Shakhtar Donetsk has left them third in their UEFA Champions League group. Nevertheless, WhoScored.com pointed to Koulibaly as one of their best performers in terms of passing:
There could be a spot to fill in central defence at the Camp Nou as of next summer, too, should Javier Mascherano leave the club. The South American is contracted to Barcelona until the summer of 2019, but he recently spoke Argentinian broadcaster TyC Sports (h/t FourFourTwo) and hinted at a potential exit:
"I have my contract to honour with the club but, obviously, once the season is over, we'll see what needs to be done. I haven't spoken to anyone about it yet.
"At Barcelona, they've always said that they're happy with me and I have time to think about it.
"It's clear that I'm playing less for my club because we have two centre-backs who are better. I am trying to battle to win my place—or at least be ready when I am called on."
The two players Mascherano, 33, refers to are Gerard Pique and Samuel Umtiti, who have each started in six of Barca's eight league games so far this season, while he has made the starting XI on four occasions in La Liga.
That dynamic may not change anytime soon, either, after Spanish football writer Andy West hailed the quality of Umtiti following last month's Champions League win over Sporting CP:
Chelsea are likely to once again pose stiff competition for Koulibaly if manager Antonio Conte returns for the Serie A man, who has developed into one of the Italian top flight's brightest stars since a 2014 move from Genk.
Barcelona demonstrated their own financial muscle with their signing of winger Ousmane Dembele in the summer, although they'll need to summon major funds once more in order to land Koulibaly.