Incoming Blues boss Antonio Conte has not been afraid to spend big so far after signing Marseille striker Michy Batshuayi for £33m.
Chelsea are now working on bringing in some defensive additions and the club have been linked with a move for Juventus stalwart Leonardo Bonucci.
But, according to Sportitalia, Conte is closing in on Koulibaly and he is ready to sanction a £34m bid in the coming days.
The Senegal international was one of the star performers in Serie A last season as he impressed at the heart of Napoli’s defence.
The 25-year-old has been linked with a move to the Premier League for over a year, but as of yet no one has been able to meet his valuation.
That may well change with Chelsea’s upcoming bid, while the English side are also ready to quadruple Koulibaly’s wages to get the deal over the line.