Antonio Conte, Manager of Chelsea applauds fans after the Premier League match between Burnley and Chelsea at Turf Moor on April 19, 2018 in Burnley, England.
Chelsea are said to be ready to back Sarri in the transfer market, while he would also earn a high salary by moving to Stamford Bridge.
The Italian has publicly been at odds with the Chelsea hierarchy since failing to sign his first choice targets last summer, including Romelu Lukaku - who ended up at United.
Napoli narrowly lost the Serie A title to Juventus this season and the effort of Sarri has caught the eye of Chelsea chiefs who endured a hard campaign with Antonio Conte.
Napoli boss Maurizio Sarri will have showdown talks with the club on Wednesday - amid links he is set to take the Chelsea job.
The Serie A club are prepared to offer Sarri a new contract worth around £3.5m-a-year, but that is not the main issue.
The Telegraph suggest that Sarri will engage in further talks with Napoli over the coming days to discuss his future in Naples, with Chelsea's next move likely to be decided by the outcome of those meetings.