Amid concern over Antonio Conte's future at Stamford Bridge, Sarri has been seen as an ideal candidate to replace his fellow Italian in west London after taking Napoli to within a whisker of the Serie A title.
Under Sarri, Napoli narrowly missed out on a first Serie A title since 1990 and it has been reported Chelsea would need to pay €8m to get him out of his current contract.
Napoli will be keen to hold on to the 59-year-old, who has guided the club to second in the Italian league.
According to the publication, by the Spanish specialist is more likely to lead the English team after another contender Maurizio Sarri has begun negotiations about prolongation of the contract with Napoli.
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Despite the claims, Conte has recently insisted that reports suggesting he is itching to make for the exit door are 'untrue'. Conte still has one year left on his £9million-a-year contract, however.
Juventus supervisor Massimiliano Allegri was one other in addition to Sarri on the membership's shortlist, with rivals Arsenal additionally curiosity as they search a alternative for Arsene Wenger.
Although they have a chance to win the FA Cup next weekend, Antonio Conte wasn't able to secure Champions League football for next season as they finished fifth in the Premier League, while they crashed out of Europe's premier competition at the last-16 stage this time round.
The Blues face Manchester United at Wembley on Saturday afternoon.