Amid concern over Antonio Conte's future at Stamford Bridge, Sarri has been seen as a ideal candidate to interchange his fellow Italian in west London after taking Napoli to inside a whisker of the Serie A title.
Napoli, however, will not impose a release clause for clubs keen to poach the 59-year-old, who was born and raised in Naples and prior to taking the job at San Paolo coached at the likes of Pescara, Perugia and Empoli.
Napoli boss Maurizio Sarri has held talks about a new contract with club president Aurelio De Laurentiis.
Their new agreement is a significant blow to Roman Abramovich and Chelsea should they elect to - as is expected - part ways with current manager Conte this summer.
Conte has been linked with Real Madrid, but Zinedine Zidane's position looks more secure than earlier in the season with the club just one victory away from a third straight Champions League win.
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.
The lack of results at Chelsea have sparked a tide of change as manager Antonio Conte will not be returning next season.
Body of Woman Pulled From Red River Identified
They want to speak with anyone who may have had contact with April Carpenter in the time she was reported missing. Her family members say they believe April Carpenter's death is suspicious because she loved life and her family.