The Blues have yet to make a signing this summer with their managerial situation having taken preference.
But away from that complicated saga, Chelsea are now closing in on their first piece of business.
On Monday, Sky Sports News reported that Napoli and Chelsea's talks were at a deadlock over Sarri's appointment as Antonio Conte's potential replacement.
Sarri worked with Rugani at Empoli but the 23-year-old's development has been somewhat stunted at Juve.
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Sarri's Napoli connection with Gonzalo Higuain could see the Argentine striker also join his former manager at Stamford Bridge. Chelsea finished a disappointing season in seventh and have missed out on competing in the Champions League next year.
Numbers were diminished due to several players' involvement in Russian Federation, but those who didn't feature in Russian Federation were put through their paces with fitness and stretching exercises.
It seems he's been offered a fresh start at Chelsea and Sarri could be eyeing the Italian worldwide as a potential replacement for David Luiz with the Brazilian star tipped for a move after falling out of favour last season.
Ancelotti is reportedly keen on both Luiz and West Ham's Angelo Ogbonna.
But one factor that is blocking Chelsea from sacking Conte this summer is the fact that they would have to pay him £9 million as compensation with his release clause for one more year.