Maurizio Sarri is in final negotiations with former club Napoli as he edges closer to taking charge at Chelsea, says the Serie A club's president.
Chelsea have also joined Manchester City in the race to sign Napoli's £50m-rated midfielder Jorginho.
Antonio Conte took charge of Chelsea's pre-season training at the weekend, despite speculation over his future.
Sarri has held talks with Chelsea, but remains contracted to Napoli, who have replaced him with Carlo Ancelotti.
"We are in the finishing line," said Aurelio de Laurentiis. "Now it depends on [Sarri] and Chelsea.
"The Sarri affair is nearly at its conclusion, it all depends on him. My lawyers have submitted papers to his lawyers."
Italian Sarri, 59, joined Napoli in 2015 and led them to second behind champions Juventus last season.
Conte, 48, has a clause in his contract that guarantees him a pay-off, thought to be £9m, for the final year of his deal.
This would be reduced if the former Italy and Juventus coach got another job, but most of the vacancies he would be interested in have now been filled.
Conte won the Premier League in his first season at the club in 2017, and the FA Cup in May this year.
Meanwhile, Chelsea have joined Manchester City in the battle to sign Italy midfielder Jorginho.
City manager Pep Guardiola identified Jorginho as his replacement for Yaya Toure, who left the club at the end of last season.
The 26-year-old indicated a willingness to join the Premier League champions, leaving City confident of completing a deal for about £50m.
However, De Laurentiis said he had concluded negotiations with City two weeks ago but that Jorginho had subsequently told him his preference was a move to London.
"If the player would rather live in London than Manchester, I can understand that," said De Laurentiis.
"I'll have to apologise to Manchester City", he added.
"If Chelsea are paying him even more, I can understand that too. Jorginho and Sarri together again? Jorginho would go to Chelsea regardless of Sarri."
Jorginho signed for Napoli in 2014 and made 36 appearances for the Serie A side last season, scoring against City in the Champions League in November.