The Blues look likely to let David Luiz depart this summer and Antonio Conte is keen to bring in defensive reinforcements.
Conte has been keeping a close eye on Rugani's progress with Juventus over the last few years and it's understood Chelsea have lodged a bid of 30million Euros.
Reports suggest that Juventus value their man at around 40 million Euros so Chelsea still have some way to go before they will be able to agree a deal.
Premier League rivals Arsenal have also been monitoring Rugani and the potential of competition could drive the fee up even further.
Rugani, who boasts seven caps for Italy, is a product of Juventus' academy and has made 54 Serie A appearances since breaking into the first team in 2013.