Rugani has a contract with Juventus until 2021 and is expected to cost in excess of £30million to lure away from The Old Lady.
The player is frustrated at his lack of playing time, however, and has experienced Sarri’s coaching before.
Both Italians spent two seasons together at Empoli, where Rugani proved a vital cog in Sarri’s defence, playing 81 games across two seasons.
David Luiz and Antonio Rudiger are currently the first-choice centre-backs under Sarri.
A move collapsed at the last minute, however, when he decided to stay in Turin.
Blues boss Maurizio Sarri is still keen on doing a deal, though.
The Italian manager will make another bid for Rugani’s services in the New Year and this time is confident of being successful.
Although Chelsea have only conceded eight goals so far this season, the pairing does not look full-proof.
The Blues were keen on landing the Italy and Juventus centre-back in the summer.
Back-ups Gary Cahill and Andreas Christensen are thought to be doubted by the new coaching staff, too, despite the latter’s emergence under Antonio Conte last term.
Rugani, 24, has also been watched by Arsenal scouts.
But they need to reduce their wage bill before they can bring anyone else in.
The Gunners did not offer Aaron Ramsey an improved contract because they do not have the resources to dish out super lucrative contracts.
Mesut Ozil takes home over £300,000 – a wage bill which defies the rest of their structure.
Meanwhile, Serie A side Roma have shown an interest in keeping Rugani in the divison.
But the fact he is taking intensive English lessons suggests where Rugani sees his future.