According to Italian outlet Tuttosport (h/t MailOnline's Sam Morshead), Juventus want to keep hold of the left-back, but he has become a "top target" for the Blues, who have seen a £55.2 million bid rejected.
The Bianconeri have reportedly told Sandro that while they hope he stays put, they "will not stand in his way if he wants to move."
Marcos Alonso did a fine job as Chelsea's left wing-back last season, but with the Blues now in the UEFA Champions League once again, they need further depth.
Sandro is of a similar quality to the excellent Spaniard, perhaps even an upgrade, and the two would have a real competition on their hands for a place in the first-choice lineup.
The 26-year-old is adept at playing left-back if Juventus opt for a back four or in a more advanced position if they go with a back three, the same role Alonso plays under Blues boss Antonio Conte.
Like Alonso, he contributes a great deal at both ends of the pitch. GianlucaDiMarzio.com's David Amoyal is a huge admirer of Sandro both going forward and defensively:
He appears to be even more effective than the Chelsea man when it comes to marauding forward. The pair contributed to a similar number of goals last season as Sandro produced three goals and seven assists in all competitions, compared with Alonso's six and three.
According to Squawka, the Brazilian played over 300 fewer Serie A minutes last year than Alonso did in the Premier League, but he nevertheless created 50 chances and completed 49 take-ons, while the Spaniard mustered 23 and 21, respectively.
He also made more successful tackles and interceptions, though he won fewer aerial duels and made fewer clearances.
Sandro is one of few players who could arguably improve on Alonso in Chelsea's starting XI, but whether he moves is reliant on how tempted he is to join the Blues and the club's willingness to part with a significant sum for what would be a relatively small upgrade to an already-strong area of the team.