The Italian club value Jorginho at £50 million but City are not willing to shell out more than £35 million on the defensive midfielder.
Confirming Chelsea are close to finally making a breakthrough, De Laurentiis said: "The Sarri deal is in the home stretch, it depends on him".
The lanky Spaniard, who joined the Blues for a club-record fee of £60 million past year, didn't have the best debut season in the English top-flight, ending the 2017-18 campaign with 15 goals in 48 appearances (all competitions).
Chelsea have been in talks with both Napoli and Antonio Conte as they try and sort their managerial situation. Chelsea's lack of Champions League football next season could tempt Hazard to look elsewhere, although he is reportedly third on Real's wishlist, behind PSG duo Neymar and Kylian Mbappe.
Thai Navy SEALs use Facebook for nail-biting updates on cave rescue mission
According to our correspondent, Thai officials have warned the rescue could take three or four days in the worst case scenario. As the monsoon rains begin, water is being pumped out of the caves and a plan is being developed to bring them to safety.
Elon Musk unveils tiny submarine to aid Thai cave rescue
On Sunday, teams of divers brought out four of the trapped boys but waited several hours before confirming their safe rescue. Rescue mission chief Narongsak Osotthanakorn on Monday said the operation on the second day started at 11am.
Woman sickened by nerve agent Novichok in England dies: United Kingdom police
Sergei Skripal and his daughter, Yulia, almost died of exposure to Novichok left on the front doorstep of Sergei's home in March . She had been hospitalised after falling ill on June 30, along with a 45-year-old man, in Amesbury , Wiltshire.
Weirdly though the sacking never came, no matter how close Roman Abramovich's side seemed to be to naming a new man in charge to take over from Conte. Conte has refused to wave the £9 million salary he is owed. But Chelsea still needs to work with Napoli to secure his release from his contract. The club would need to pay at least another £5m in salary for Sarri.
Conte has been overseeing Chelea's preseason training preparations.
Chelsea are preparing for their first pre-season fixture against Perth Glory on July 23 before they venture off for the International Champions Cup where they do battle with Arsenal, Inter Milan and Sevilla. This is a make or break summer for the England global; he can either leave and fulfil his potential elsewhere or give it one more shot at Chelsea. Adding Sarri may not be the quick fix Chelsea hope to make.
Several players have been left in limbo due to this question mark, with David Luiz one of the players expected to report back on Monday, though his relationship with Conte is strained.