The Blues are expected to announce the appointment of former Napoli boss Maurizio Sarri in the next week with Antonio Conte leaving the club.
The uncertainty over the club’s next manager has slowed progress on transfer targets but Sarri is keen to hit the ground running in west London and has worked with Rugani before.
The 23-year-old started just 22 Serie A games last season and Chelsea hope to sign him after submitting a £35m bid, according to the Evening Standard.
Chelsea have promised to double Rugani’s weekly salary to around £30,000-a-week and have offered him a five-year deal at Stamford Bridge. Rugani’s arrival could spell the end of David Luiz’s second stint at the club as Chelsea look to cash in on the Brazilian.
Luiz barely featured under Conte last season as he struggled with injury and Chelsea believe they could recoup much of the £30m they spent on him in 2016.