It is understood United can meet the 20-year-old's personal terms, but there is no agreement over a fee, BBC Sport reported.
United boss Ole Gunnar Solskjaer wants another wide player and the club is considering alternative targets.
Real Madrid's Wales forward Gareth Bale and Inter Milan's Croatia international Ivan Perisic, both 31, are two names that have been mentioned.
Dortmund want over £100 million for Sancho, who was signed from Manchester City for £10 million in 2017. United does not feel a deal is possible at that valuation.
The Premier League club is losing about £5 million for every match played at Old Trafford behind closed doors amid the coronavirus pandemic.
The transfer window closes on October 5.