According to a report from French website Paris United, both clubs are looking to strengthen the left-hand side of their defence and have identified Sandro as their number one target.
The 27-year-old has made 114 appearances for Juventus since joining the Serie A side in 2015 and has helped the club win three Serie A titles and three Coppa Italias during his time in Turin, as well as finishing runners-up in the Champions League in 2015.
Paris Saint-Germain are looking to bolster the left-back position, with Lavyin Kurzawa the only recognised left-back currently in their squad. This follows the departure of Yuri Berciche, who made 32 appearances for the club last season before moving to La Liga side Athletic Bilbao earlier this month.
Meanwhile, Manchester United are looking to strengthen in the same position due to rumours surrounding the future of Luke Shaw. He has been heavily linked with a move away from Old Trafford, although a recent report claims that he has turned down a move to Premier League rivals Everton.
Similarly to PSG, United have also agreed personal terms with Sandro on a provisional basis, although have refused to meet the price tag for the Brazil defender. The deal has been complicated, though, by Shaw's reluctance to leave Old Trafford - which gives PSG the lead in the race for the Brazilian defender's signature.
Alex Sandro remains the top priority of Thomas Tuchel, as he has not spoken to Juventus regarding his future at the Turin-based club so remains open to a move to the French capital.
Meanwhile, United will remain short for strong left back options, with Ashley Young, a right footer, as well as defenders Daley Blind and Marcos Rojo the only current United players capable of playing in that position.