However, Conte's apparent dismissal drew a response from Chelsea's Cesc Fabregas, who liked a tweet a Chelsea fan posted about Conte having been sacked although the Spanish 2010 World Cup victor subsequently claimed he had liked it by accident.
Conte departs Chelsea after two seasons, winning the Premier League in his first campaign.
Former banker Sarri, 59, will be Chelsea's ninth full-time manager since Roman Abramovich bought the club in 2003.
The Serie A side have appointed Carlo Ancelotti as their new manager, and while Sarri is still on their books, he has been strongly linked with a move to Stamford Bridge to replace Antonio Conte. "My lawyers are in talks with his lawyers to finalize everything".
The Blues finished fifth in the Premier League, failing to qualify for the Champions League.
It now appears that Cesc Fabregas is one Chelsea star who wouldn't have been particularly upset by his departure, liking one tweet that simply said "Yessssssss Conte gonnnnnnnnnnnnnnn @CFC".More news: Lawyer: Charges Against Stormy Daniels Dropped
Chelsea are likely to pay around £50m, with further fees due in bonuses, to secure the Italy midfielder Jorginho and Sarri.
He may decide that he wants Blackman to stay around and gain experience of being in the first team at the Premier League club.
It is harsh these days how football club owners are dealing with managers, even though there are high expectations and financial deals that could be affected, it leaves an adverse image on the club.
With Jorginho at his disposal, Sarri should be able to replicate most of that system from Napoli, which might help guide Chelsea back into the top four.