An agreement was reached late on Thursday evening after talks between senior officials. A deal could be completed as early as Friday.
It is understood a compensation fee in excess of £5m has been agreed.
Sarri arrived from Napoli in July 2018 and led the Blues to third place in the Premier League and won the Europa League in his one season in charge.
Despite signing a three-year deal last July, he will become the ninth full-time manager to leave the club under Chelsea owner Roman Abramovich.
Throughout the 60-year-old Italian’s time at Stamford Bridge there was repeated speculation about his position, with Chelsea fans expressing their discontent at tactics and team selections.
One of the low points came in February when goalkeeper Kepa Arrizabalaga challenged his authority by refusing to be substituted in the Carabao Cup final at Wembley, shortly before Chelsea were beaten in a penalty shootout by Manchester City.
But Sarri did manage to win his first ever trophy as manager with a 4-1 victory over Arsenal in May in the Europa League final, and after the match said “he deserved” to stay with the club.
Chelsea are currently unable to sign any players after they were banned for two transfer windows by Fifa – a decision they are appealing at the Court of Arbitration for Sport.
Their star player Eden Hazard has joined Real Madrid for a fee that could exceed £150m.
Significantly, Chelsea have not asked for the suspension to be put on hold until a final decision is reached. It means their only new arrival might be USA forward Christian Pulisic, a £58m signing from Borussia Dortmund in January, who spent the remainder of the campaign on loan in Germany.
Juventus are managerless after Massimiliano Allegri left at the end of last season, having won the league title in each of his five seasons since taking charge in 2014.
Sarri’s year at Stamford Bridge
After earning glowing references for his tactics at Napoli, he looked to have effectively introduced ‘Sarri-ball’ to his new players as Chelsea started their Premier League campaign with a 12-game unbeaten streak.
But the Blues were out of title contention after losing three out of four Premier League games from January to February, including a 6-0 defeat at eventual champions Manchester City, which saw them slip to sixth in the table.
Chelsea then lost 2-0 at home to Manchester United in the FA Cup, when fans booed the Italian’s substitutions and joined in when the visiting supporters sang “You’re getting sacked in the morning”.
However, Sarri remained in charge, and of the 19 matches played after they were beaten on penalties in the League Cup final, his side lost just two, as they won their first European trophy since securing the Europa League in 2012-13.
They also held off the challenge of Tottenham, Arsenal and Manchester United to finish third in the league and clinch Champions League qualification.
Analysis – who could Chelsea turn to?
For all the difficulties Chelsea managers tend to encounter, there has been no shortage of potential candidates being linked to the job.
The most obvious is Blues’ record scorer Frank Lampard.
Lampard ended his first season as a manager with defeat at Wembley in the Championship play-off. Lampard is steeped in Chelsea history, won 11 major trophies during his 13 years at the club, and is adored by supporters, even though he eventually moved away to join Manchester City before ending his career in Major League Soccer with New York City.
At Derby, Lampard also linked up with former team-mate Jody Morris, who developed an impressive reputation during five years working with Chelsea’s youth teams – that might improve the pair’s chances even more, given the transfer embargo Chelsea are facing.
Chelsea loanees Fikayo Tomori, Mason Mount and Tammy Abraham were all involved at Wembley and others, such as Reece James, have also impressed in season-long moves away from the club.
Morris’ inside knowledge would be a major asset in deciding which of these youngsters have the capability to step into the first-team picture.
It is also probable, although by no means certain, that Lampard would be given time if results did not go well.
Rafael Benitez, whose Newcastle future is uncertain, is also tipped, despite the fact Chelsea’s fans have no love of the 59-year-old, something they made clear during his six months in temporary charge following the dismissal of Roberto di Matteo in 2012, when fans made banners demanding his exit even though he won the Europa League.
Wolves manager Nuno Espirito Santo is also of interest. Santo has taken Wolves from the Championship to seventh in the Premier League – and European qualification – in the space of two seasons. He is known to be hugely ambitious and for all the promise Wolves have shown during his time at Molineux, Chelsea still represents a significant step up.
And, given Chelsea have already had six Italian managers and he has won five Serie A titles in a row, Massimiliano Allegri cannot be discounted, even if the 51-year-old has said he intends to take a year out of football.