Conte looks certain to leave Stamford Bridge at the end of this season, after just two years in charge.
Sarri, an Italian like Conte, has emerged as a serious contender after inspiring hometown club Napoli, to threaten the dominance of perennial Italian champions Juventus.
The 59-year-old is understood to have a £7million release clause, valid until May 31, in his contract.
Talks over a new deal have stalled, with Sarri not ready to make any decisions until his team play leaders Juventus in a title decider next weekend.
Napoli sit second in Serie A, four points behind with just two defeats in their last 12 games.