Sky Sport Italia, as quoted by the Daily Express, is claiming that the west London side have failed in their latest attempt to bring the full-back to Stamford Bridge.
The Blues are thought to be on the lookout for a number of new signings this summer and full-back is one area which Antonio Conte is thought to be keen to strengthen ahead of next season.
And it is claimed that the west London side have failed in their initial offer to try and tempt Juve into selling the Brazilian defender this summer.
The same report claims that Juve are keen to keep hold of Sandro and want to offer him a new contract to try and convince him to stay at the club.
Chelsea confirmed their third signing of the summer on Saturday when they announced a deal to sign midfielder Tiemoue Bakayoko from Monaco.
The Blues have also brought in goalkeeper Willy Caballero and defender Antonio Rudiger this summer as Conte prepares for his second campaign in charge at Stamford Bridge.
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