The 19-year-old departed the Etihad in 2017 to join the German giants and has excelled at Signal Iduna Park.
United were heavily linked with a move for the England international over the summer but a switch failed to materialise.
According to Sport Bild, they will face serious competition from the Premier League and further afield next summer.
Dortmund are said to be prepared to lose Sancho next summer, despite having a contract until 2022.
The Bundesliga side are already at work finding a replacement for him, with Hertha Berlin’s Javairo Dilrosun a possible target.
Dilrosun is another former Manchester City youth player and departed the club in 2018 for the German capital.
Sancho is said to be valued in excess of €100 million after dazzling Bundesliga crowds during his time at Dortmund.
He already has three goals and six assists to his name in just eight league appearances this season.
Last term, the teenager provided 13 goals and 19 assists in all competitions for BVB and earned international recognition.
Sancho made his senior Englad debut against Croatia in October 2018 and has since become an important part of Gareth Southgate’s squad.
Over the last year, the winger has scored twice and provided three assists in 10 caps for his country, with both goals coming in the 5-3 win over Kosovo in Euro 2020 qualifying in September.
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