The Blues are desperate to bolster their defence, following the exits of Antonio Rudiger and Andreas Christensen.
Koulibaly, 30, fits the bill - but the West Londoners will have to agree a fee with Napoli.
According to Gazzetta dello Sport, the Serie A side are demanding £34m for their star defender this summer.
Koulibaly has just one year remaining on his Napoli contract - with talks over an extension having stalled.
The Senegalese star currently earns around £100,000 a week in Italy.
Remarkably, club chief Aurelio De Laurentiis' latest offer would have seen this DECREASE to £65,000 a week.
With talks at an impasse Koulibaly looks likely to be available on a free transfer next summer, unless a club matches Napoli's asking price this year.
Chelsea are willing to offer the defender around £165,000 a week to join this summer.
Paris Saint-Germain are also keen on recruiting the in-demand defender.
Koulibaly is International teammates with Chelsea goalkeeper Eduard Mendy.
The duo both helped Senegal win the Africa Cup of Nations earlier this year.
In addition to Koulibaly, the Blues have also been linked with Sevilla ace Jules Kounde and RB Leipzig's Josko Gvardiol.
Further forward, Chelsea are chasing Raheem Sterling and Ousmane Dembele.
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