The Daily Mirror is claiming that the west London side have “sounded out” the 59-year-old about the possibility of him taking over from Antonio Conte at Stamford Bridge in the summer.
The same report says that Chelsea FC are extremely likely to part company with Conte at the end of the season after two years in charge at the west London club.
According to the same report, Sarri is understood to have a £7m release clause in his contract, which is valid until 31 May.
The same story says that talks over Sarri signing a new deal at Napoli have stalled, and that he is unwilling to make a decision about his future right now.
Chelsea FC are believed to be on the lookout for a new manager after a disappointing campaign under Conte this term.
The Blues are currently in fifth place in the Premier League table and look set to miss out on a spot in the Champions League for next season.
The west London side will return to Premier League action when they take on Southampton on Saturday lunchtime.
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