Chelsea football club are allegedly accusing Conte of breaching his contract after confirming the end of his employment on Friday morning.
During three years with Napoli, Sarri has not won a major honour but has guided the club to finishes of second, third and second again - behind Juventus in 2017-18.
But, despite winning the FA Cup last season - beating Manchester United in the final, Chelsea have ditched Conte ahead of the new campaign.
Conte's average of 2.14 points per game in the Premier League is bettered only by Alex Ferguson (2.16) and Guardiola (2.34).
Chelsea are expected to announce Sarri's appointment on an initial two-year contract imminently - together with the signing of Italy global midfielder Jorginho for a combined fee of €65 million (£57.5m) - after convincing Napoli chairman Aurelio De Laurentiis to release the 59-year-old from his contract.
The Italian was an inspired choice in that first season, taking Chelsea from 10th to champions and captivating Stamford Bridge with his fiercely driven approach and animated body language that pleased the club's support, captivating crowds around the Premier League.
Two trophies in two seasons but the writing was on the wall.
Napoli are also expecting compensation of around £4.5million for Sarri, who is under contract even though he is no longer their coach.
He also clashed with senior players such as Diego Costa and David Luiz while others had begun to grow tired of his methods.
The former Empoli boss is not known as a big spender which might fit with the slightly more modern Chelsea era of tighter spending. Attention will then turn towards securing Sarri and Chelsea's other summer targets, believed to include players such as Aleksandr Golovin and Daniele Rugani.