However, his future at Stamford Bridge remains uncertain as, despite winning the FA Cup, they finished fifth in the last campaign and failed to qualify for the Champions League.
"Sarri is close to being new Chelsea manager," De Laurentiis told reporters during the unveiling of new Napoli manager Carlo Ancelotti.
"My lawyers are in talks with his (Sarri) lawyers to finalise everything."
Sarri was replaced by Ancelotti in May with the Naples club seeking to end Juventus' dominance in the league.
The 59-year-old Sarri led Napoli to two second-place and one third-place finish in three seasons in charge at the club.
Chelsea declined to comment on the issue when contacted by Reuters.
Conte has one year remaining on his current contract and has already taken charge of the club's pre-season preparations at their Cobham training ground.
(Reporting By Arnab Paul in Bengaluru; Editing by Christian Radnedge)
