The Brazil international was a primary target for the Blues manager Antonio Conte, who wanted to bolster his side's defence. The 26-year-old was identified as a player to strengthen the left wing-back position. But the west London club's multiple approaches were turned down by the Old Lady.
According to the Mirror, Sandro is still a priority target for the former Juventus and Italy manager. They will make another approach in bringing the defender to Stamford Bridge by pushing through a £50m ($68m) deal.
Chelsea's former manager Jose Mourinho is also believed to be interested in signing Juventus star for Manchester United. The Blues have already made an approach in order to beat the Red Devils in signing Sandro.
It is believed that Juventus are open to the idea of allowing the South American defender to leave the Allianz Stadium in January months after having fought hard to keep him at the club. The Turin club have already identified Bayer Leverkusen's Wendell as Sandro's replacement.
The Premier League winners currently have the services of Marcos Alonso as the only recognised left wing-back in the squad. Should they sign Sandro, the Brazilian's arrival will provide more competition at Chelsea in the same position.
Juventus director general Giuseppe Marotta has already admitted the club will not stand in the player's way if he decides to leave the Serie A winners.
"We have said many times that when a player asks to be sold, regardless of prestige or importance within the team, we are in favour of a sale. When a player is unsatisfied, it is better to let him go," Marotta explained.
Meanwhile, Conte has also opened the door for new arrivals after stressing that Chelsea will complete signings in the January transfer window, if it can help them "improve" the squad.
"At the moment, I am ready to continue working to play will all these players. They are showing me great commitment and I am very happy to work with these players. At the same time, if there is the possibility to improve our squad, I think the club will try to do this," the Chelsea manager said.