As the new league season approaches, Chelsea's non-World Cup players returned to their Cobham facilities on Saturday morning for their first pre-season training session and standard procedure medical checks.
Chelsea plan to replace Conte with Maurizio Sarri and have been in talks to extricate the 59-year-old from his contractual obligation to Napoli for more than a month, but the situation remains unresolved.
As for Conte, it will cost Chelsea £9 million to jettison him, as that is how much he is owed for the final year of his contract.
"[Sarri to Chelsea] is about to happen, it just depends on him", De Laurentiis said after a news conference to introduce Carlo Ancelotti as Sarri's replacement.
And Napoli's president also revealed that moving to Stamford Bridge alongside Sarri will be Italian midfielder, Jorginho. I've laid down my conditions.
City had been aiming to complete a £50 million (€56m/$66.3m) deal to sign Jorginho , with De Laurentiis confirming he has accepted an offer from the Premier League champions.
Incoming Chelsea manager Maurizio Sarri expects to be formally appointed by the club on Monday, finally bringing a welcome end to one of the summer's longest running sagas.
Manchester City have been unwilling to match Napoli's financial demands and there are indications the Citizens feel by dragging Chelsea into the affair, the Serie A giants are trying to put pressure on them.
The Blues have reportedly lined up Sarri to replace current boss Antonio Conte following their poor Premier League title defence and failure to qualify for next season's Champions League.