Sarri's agent was recently spotted in London although, with an €8 million (£7m) clause in his Napoli contract, the Serie A title challengers are keen to renew his deal.
His £1.2m salary presents an opportunity for teams to secure him, with several major clubs across England and the rest of Europe looking to sign a top manager this summer
Ex-Barcelona boss Luis Enrique is another candidate for the job and Chelsea are simultaneously looking to replace the club's former technical director Michael Emenalo, who left for Monaco in November.
That replacement might not be a like-for-like change but it will be to provide a link between the head coach and the board. Ex-player Juliano Belletti is understood to be one name that's being considered for the position.
Conte has repeatedly denied that he is set to leave Chelsea when questioned, but it is still widely believed that he is set for the exit door.
Italy's football association is believed to have tried to bring him back for the national team, whom he left for the Blues after Euro 2016.
Paris Saint-Germain also previously considered Conte for their soon-to-be-vacant role after Unai Emery announced his exit, but ex-Borussia Dortmund coach Thomas Tuchel is thought to be on the verge of taking that job.
Chelsea are still battling to secure a Champions League spot for next season, although it is looking difficult to achieve and they have an FA Cup final to come against Manchester United.
Conte is keen to focus on a positive end to the season, but there is a lack of clarity over where he may be managing next season.