The former Manchester City winger is a priority target for both Frank Lampard and Ole Gunnar Solskjaer but it is understood United are currently front of the queue for the 20-year-old.
However, with the transfer window currently up in the air due to the suspension of leagues because of Covid-19, there is potential for the situation to change and it is understood that no agreement has yet been reached with any club for the sale of Sancho.
Dortmund are reportedly already planning for life without the England star, who has remained tight-lipped about his long-term future. He was quizzed about a potential return to the Premier League earlier this month but refused to be drawn on a transfer back to England.
It is understood Dortmund want €130 million (£115m/$143m) for Sancho and their chief executive Hans-Joachim Watzke has warned that they will not be willing to accept a cut-price offer for the winger.
“I can clearly say that despite the existential crisis [for football] even the richest clubs don't have to believe they can go bargain hunting at Dortmund,” Watzke told Bild . “We must not sell anyone below value.
“Even before the coronavirus outbreak, we said that we prefer that Jadon stays with us. At the end of the day, however, you always have to respect what the player wants.”
Boyhood Chelsea fan Sancho, who is close friends with Tammy Abraham and Callum Hudson-Odoi, left Manchester City in 2017 for Germany and has been a success in the Bundesliga, but disciplinary issues at the start of the year led to speculation the attacker could be on his way.
United were interested when Jose Mourinho was in charge back in 2017 but Sancho decided to make the move to Germany instead. City have the right to match any bid accepted by Dortmund for the winger but there is no clause in his contract that would stop him from joining United.
Both Chelsea and United are keen to strengthen their attacking line whenever the transfer window opens again.