The Stretford club's scouting department identified the former Manchester City youngster as a possible signing when Jose Mourinho was in charge. Ole Gunnar Solskjaer and his assistant manager, Mike Phelan, subsequently encouraged United to act on their interest.
But Dortmund have spurned United's inquiries about Sancho and maintain a tough stance despite signing Thorgan Hazard and Julian Brandt on Wednesday. Christian Pulisic completed his permanent transfer from Der BVB to Chelsea when the Bundesliga season ended.
Ending the hunt for Sancho could accelerate United's negotiations for Daniel James, who should cost around £15 million to acquire from Swansea City. United are also understood to be eyeing Newcastle United's Sean Longstaff and Atletico Madrid's Saul Niguez.
There could also be a defensive overhaul on the horizon at Old Trafford, as Leicester City's Harry Maguire and Napoli's Kalidou Koulibaly have reportedly emerged as potential recruits. Towering Ajax defender Matthijs de Ligt, meanwhile, seems to prefer a switch to Barcelona.