At the end of last season, Sarri's managerial reign at Napoli came to an end but any club interested in the Italian's services must first agree a compensation deal with the Serie A outfit.
Chelsea have been forced to remain patient in their efforts to replace Antonio Conte in the Stamford Bridge dugout but it now appears that an announcement is not far away.
On Wednesday morning, De Laurentiis said: "Sarri is close to be new Chelsea manager. My lawyers are in talks with his lawyers to finalise everything."
Should a deal be completed, Chelsea must also pay up the remainder of Conte's contract, which is due to expire in 2019.