Sky Sports says Dortmund are demanding a fee in excess of £100million for the England international and United have a sustained interest in the 20-year-old.
But United are not willing to bid any more than half of that asking price.
Their stance is likely to see them miss out on Sancho, unless the winger remains with Dortmund this summer and moves at a later date.
Both clubs remain significantly far apart in their valuation of Sancho, who has 20 goals and 19 assists in all competitions this season.
On Monday, Dortmund informed the German stock market that matches being played behind closed doors will lead to losses of £41million.
That could offer United a sign of encouragement that the club may look to offload top stars at a cut price.