According to Metro, Koulibaly is top of Sarri's transfer wishlist and might become the most expensive signing in Chelsea's history, ahead of Alvaro Morata.
The Stamford Bridge outfit are set to spend up to €85 million to unite the Senegalese defender with his former boss in London.
After a string of impressive defensive displays with the Partenopei this campaign, the 26-year-old is back on the radar of the 2017-18 FA Cup winners.
This season, Koulibaly featured in 35 league matches averaging 1.5 tackles per game and 3.2 clearances per game.
The centre-back also scored crucial goals for the Stadio San Paolo outfit which earned him praise from football great Diego Maradona.