Sarri is keen for a move to Chelsea and his enthusiasm for the job has allowed him to become the front-runner ahead of former Barcelona coach Luis Enrique, whose higher wage demands make him a tougher appointment.
Zenit St Petersburg have also made an offer to Sarri, but he is delaying his response in the hope that officials at Stamford Bridge activate his £7 million ($9.3m) release clause.
Napoli chairman Aurelio De Laurentiis is already in talks with Carlo Ancelotti to replace Sarri at the Stadio San Paolo after failing to receive an answer following post-season talks to renew the 59-year-old's contract.
In addition to Sarri, Chelsea have also been linked with Fulham's Slavisa Jokanovic but he appears to be an outsider for the job, while Monaco have confirmed that Leonardo Jardim will stay in his post, despite Portuguese super-agent Jorge Mendes taking an interest in placing him at a new club.
Conte's exit from Chelsea after winning two trophies in two seasons is due to fraught relationships with the club's board, and he has also left some of his squad feeling either unhappy or indifferent towards him.
Gary Cahill and Thibaut Courtois have admitted that the speculation around Conte’s future had unsettled the team's efforts to qualify for the Champions League after Chelsea missed out on a top-four finish.
Former Juventus coach Conte will be due a £9m pay-out for the duration of his contract upon his departure from Chelsea, but that will stop if he takes another managerial role.
However, with there currently no suitable vacancies for Conte, the Italian may decide to take a break once his Chelsea departure is confirmed.