Italian news outlet TuttoMercatoWeb say the centre-back is at the top of Conte’s wish list.
The former Juventus chief is determined to land Koulibaly having missed out on him last summer.
“Napoli defender Kalidou Koulibaly has been linked with Chelsea”
Chelsea are in the market for a centre back with club captain John Terry expected to see his Stamford Bridge career come to an end in the summer.
The former England skipper, 36, has been linked with big-money moves to America and the Chinese Super League.
Conte has been using a back three of Cesar Azpilicueta, David Luiz and Gary Cahill to great effect and also has Kurt Zouma to call on.
But he’s expected to source a long-term replacement for Terry – and a move for the Senegal international could fit the bill.
Koulibaly has dazzled for Napoli since joining the club from Genk in 2014.
He’s racked up 75 appearances for the club, scoring two goals.