Rai Sport, as quoted by talkSPORT, is reporting that the Serie A runners up are worried about losing their star full-back in the summer transfer window.
The same article states that Napoli expect Sarri to move to sign the Algeria international if the former Napoli boss does take over the reins from Antonio Conte.
According to the same story, the 24-year-old would be keen to work with Sarri at Chelsea FC given his success under the Italian coach at the Naples club.
Hysaj has made one assist in 35 appearances in the Italian top flight last term to become a key member of the Napoli team.
Only Pepe Reina and Jose Callejon racked up more Serie A minutes than the Algerian defender in the Italian top flight last season to highlight his importance to Sarri.
Chelsea FC finished in fifth spot in the Premier League table last term to miss out on a Champions League place for the second time in three seasons.
The Blues were 1-0 winners against Manchester United in the FA Cup final at Wembley last term.
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