Napoli's president revealed Sarri was close to finalising a deal to take over at Chelsea on Wednesday, two days before Conte's sacking was confirmed by the Premier League club.
Chelsea legend Gianfranco Zola is expected to be Sarri's right-hand man at the club but according to Sky Italia, as cited in a report from Calciomercato, the Blues had approached Martusciello to gauge his interest in joining the club.
Winning the FA Cup against former Chelsea manager Jose Mourinho's Manchester United in May was scant consolation to finishing 30 points behind champions Manchester City in the league.More news: Antonio Conte sacked by Chelsea
The 48-year-old Italian, who had a year left on his contract, took pre-season training earlier this week. "I wish you every success in the future". He had been waiting since winning the FA Cup in May to resolve his future at Stamford Bridge, but difficulty in securing Sarri delayed the process.
There was concern at the club that if Conte stayed then star players could try to leave, including Real Madrid target Eden Hazard. Conte's relationship with Chelsea's hierarchy was strained after disagreements over their transfer policy last season.More news: Will Smith smashes Drake's #InMyFeelingsChallenge on Budapest bridge
Sarri, 59, led Napoli to two second-place and one third-place finish in three seasons in charge.
Chelsea seeks a 13th permanent manager under Abramovich's ownership, and at possibly the most turbulent period of the Russian billionaire's trophy-filled reign.
Sarri didn't win a major title at Napoli, however, and that would not be tolerated at Chelsea.More news: Trump administration slashes more ObamaCare funds