The Blues are prepared to pay around £44m for his signature but are also looking to get his team-mates Higuain and Pjanic on board too.
Sarri is a long-term admirer of the pair and believes they would add quality to his attacking options already available.
Chelsea have already received a boost in their pursuit of Pjanic with Manchester City dropping out of the race to sign him but the 28-year-old Bosnian will not come cheap.
Meanwhile, Davide Torchia, Rugani’s agent, admits there is interest from the Blues but any negotiations for the defender and Higuain are separate.
He said: “The interest from Chelsea is there for Rugani. Beyond the figures though there’s a technical question, neither the player nor Juventus have ever said they want a sale.