Conte was reported to have left the club on Thursday, after two seasons at Stamford Bridge.
Chelsea have been strongly linked with Sarri over the past two months but previous head coach Antonio Conte was only removed from his position on Friday.
A new contract worth over £300,000-a-week remains on the table, but there is a feeling around the 27-year-old that, following such a good World Cup, that it is time for a new challenge.
Conte also fell out with David Luiz and Willian, and used press conferences last season to accuse the board of not signing his targets. "In the title winning season, the club set a then-record 30 wins in a 38-game Premier League season, as well as a club-record 13 consecutive league victories", it said. "Great man, Great manager".
Serie A players Maurizio Sarri could bring to Chelsea
Sarri could be followed by midfielder Jorginho from Napoli, with Chelsea willing to pay £50m, plus £7m in bonuses, for the pair. In May, Napoli appointed Carlo Ancelotti to replace Sarri amid speculation that the latter could take the Chelsea job.
"We wish Antonio every success in his future career", the statement read.
Trophies: Premier League 2016/2017, FA Cup 2018.
Sarri has been favourite to succeed his compatriot after impressing as manager of Serie A side Napoli, who have replaced him with former Chelsea handler Carlo Ancelotti. Conte's relationship with Chelsea's hierarchy was strained after disagreements over their transfer policy last season.
This text will now form the basis of Chelsea's evidence against their former manager. Sarri and Higuain worked together at Napoli.
He also clashed with senior players such as Diego Costa and David Luiz while others had begun to grow tired of his methods.