The Blues can still go out on a high this season, nevertheless, by trumping former manager Jose Mourinho and his United side in Saturday's FA Cup final at Wembley.
Chelsea FC won the Premier League title with two games to spare last season after the Blues managed to see off competition from Tottenham Hotspur. Conte is expected to leave Stamford Bridge this summer and Sarri is the favourite to step into his shoes.
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.
In an ideal world, Aurelio De Laurentiis, Napoli's president, would keep Maurizio Sarri around for the foreseeable future, and that's what he's now working towards.
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.
That would centre on an improvement in Sarri's salary, with Sky reporting the Coach stands to earn €3.8m a year plus bonuses and his release clause revoked.
Chelsea have already moved away from Enrique previously due to concerns over the Spaniard's excessive wage demands.
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