As revealed by Goal, Chelsea have made contact with Sarri as they weigh up their potential candidates to replace Antonio Conte, with the Italian having guided Napoli to their second runners-up finish in three Serie A seasons.
The 59-year-old, who has an €8m release clause in his contract, has held talks with outspoken president Aurelio De Laurentiis over his future.
Russian giants Zenit have reportedly offered €4m per season to lure Sarri to the club following Roberto Mancini's departure, while he has apparently been lined up as a replacement for Mauricio Pochettino, should he leave Tottenham.
De Laurentiis has also hinted that Sarri might be on his way out of the Serie A club after saying "time has run out", while the manager's own post-match comments after the final match of the season also seemed to suggest he was soon to depart.
However, Sarri's agent Alessandro Pellegrini has insisted there have been no offers for the Napoli boss, stating that any interested parties will need to pay the release clause to get their man.
"Could Sarri leave? For a club to appoint him, they need to pay his €8m release clause."
Napoli ended their season with a 2-1 win over relegated Crotone on Sunday as they finished four points adrift of champions Juventus.