Chelsea boss Maurizio Sarri has only made two signings since his appointment – Jorginho and Rob Green – and Rugani tops his wishlist.
The Blues have been working hard on trying to prise the defender away from Serie A with reports last week claiming the 23-year-old had agreed a five-year deal worth £77,000 a week.
However, a deal has failed to be pushed over the line and Chelsea now face strong competition from Madrid.
According to Spanish publication OK Diario, Madrid have been in talks with Juve chiefs for weeks.
CHELSEA TRANSFER NEWS: GRANOVSKAIA JETS OUT TO COMPLETE THREE DEALS
The report claims during negotiations for Cristiano Ronaldo – who left Madrid for the Allianz Stadium earlier this month – the defender’s name has been discussed.
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With Juve and Madrid having a strong relationship following the smooth transition of Ronaldo’s departure, the Serie A champions could be willing to do business again over Rugani, leaving Chelsea to miss out.
Madrid will have Ronaldo to thank if they can snatch Rugani from under Chelsea’s nose with the Portuguese’s transfer opening up a strong bond between both clubs.
However, it remains to be seen if Rugani will actually leave Juve after his agent, Davide Torchia, stated the player is happy in his homeland.
“The interest from Chelsea is there for Rugani,” Torchia told Radio Sportiva.
“Beyond the figures though there’s a technical question, neither the player nor Juventus have ever said they want a sale.
“The operation with Chelsea is separate from [Gonzalo] Higuain, each deal has a different cost and different dynamics.
“The two players can bring in different profits. Rugani is calm and happy, he’s at the pre-season training camp and he’s thinking about Juventus.”