Following the departures of Antonio Rudiger and Andreas Christensen, Koulibaly has emerged as one of Thomas Tuchel's primary targets ahead of the new campaign.
Recent reports have claimed that the Blues have made significant progress in their pursuit of the 31-year-old, while the defender himself has revealed that a potential switch to Stamford Bridge is "on the right track."
According to journalist Fabrizio Romano, Chelsea have now reached an agreement with Napoli to sign the Senegal international for an initial €40m (£33.8m) plus add-ons, with the defender also agreeing personal terms on a £8.5m-a-year salary.
Romano adds that Koulibaly will fly to London on Wednesday evening before undergoing his medical in the capital on Thursday ahead of finalising his switch to the Premier League club.
Koulibaly, who has just 12 months remaining on his Napoli contract, has spent the last eight seasons with the Serie A outfit, making 317 appearances across all competitions as well as winning both the Coppa Italia and Supercoppa Italiana.
Koulibaly could become Chelsea's second signing of the summer window following confirmation of Raheem Sterling's £47.5m arrival from Manchester City on Wednesday, while Nathan Ake could become their third addition as the Blues have allegedly agreed a £45m fee with the Citizens to sign the Dutchman.