Sarri will be confirmed as Chelsea’s new head coach as soon as the club reach a compensation agreement with Napoli and their current coach, Antonio Conte. But, with just over six weeks left of the transfer window remaining, Chelsea have yet to make any signings.
The club have been in talks with Sarri’s representative Fali Ramadani for several weeks about the 59-year-old taking over from Conte and an attempt to sign Rugani has been discussed.
The Italy international played under Sarri during an impressive two-year loan spell at Empoli between 2013-15 before establishing himself in the first team at Juventus.
But Rugani, who has three years remaining on his contract, started only 22 games in Serie A last season and is prepared to move.
At 23, he fits Chelsea’s transfer policy profile but they still face a tough task convincing Juventus to sell.
However, the Blues are preparing a five-year contract worth around £60,000-a-week - double what Rugani earns in Turin - to entice him to Stamford Bridge.
Rugani’s arrival could also see senior players like David Luiz, who started just nine League games due to various injury problems last season, leave.
Sarri is believed to have agreed a contract with Chelsea last month, but has had to wait while the Blues negotiate with Napoli for his release, as well as with Conte over his departure.
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Napoli, who have already hired Carlo Ancelotti to take over from Sarri, are ready to accept £4.5m to release the latter from the two years remaining on his contract.
Chelsea have still to cut a deal with Conte but the matter is expected to be resolved so that Sarri will be in place for the start of pre-season training, which begins on July 9 for players not involved in the World Cup.
Conte has made it clear to Chelsea that he will not leave unless he is paid the £9.5m due for the final year on his deal.
Chelsea have also been monitoring Newcastle centre-half Jamaal Lascelles.