Chelsea's club policy when it comes to managerial departures is they pay said-manager until they find a new job, but Conte is prepared to take time off, which could cost the club £9 million.
Sarri won plaudits for the expansive passing football his Napoli team played in the three seasons he was in charge, but he failed to halt Juventus' dominance of Serie A and ended his spell in southern Italy without a trophy.
He ran into trouble with his employers after his first season at the Stamford Bridge but managed to wrap up the 2017-18 season with silverware - beating Manchester United to win this year's FA Cup.
That came a day after Napoli president Aurelio de Laurentiis said Jorginho favoured a move to London.
Their willingness to beat Manchester City's offer for Italy worldwide midfielder Jorginho provided the belated breakthrough in talks.
"I hope Chelsea will continue to be successful and I wish everyone well for next season".
The 26-year-old Jorginho, who has played eight times for Napoli, had more touches per minute than any player in Europe's top five leagues last season.
Chelsea announced this morning that Conte has finally been relieved of his duties after months of speculation surrounding his future.
Chelsea have parted company with their Italian manager Antonio Conte after two years at Stamford Bridge, the Premier League club said on Friday.