Sancho is United’s priority transfer target but the two clubs remain in talks to agree a fee, with Dortmund holding out for a deal worth up to €120 million (£108 million), The Independent reported.
The Bundesliga club set a deadline of August 10 for United to table its final offer, as Dortmund wants time to replace Sancho during the current window.
Senior United sources described that deadline as “artificial” last week and viewed it as no barrier to completing what is likely to be the Old Trafford club’s record signing.
United views Dortmund’s €120-million asking price as unrealistic in the current climate and has not ruled out walking away from the negotiations if an agreement cannot be reached.
Any deal is all but certain to be structured in installments and performance-related payments, though the two clubs are yet to agree how much United should pay as an initial fee.
Last week, Dortmund chief executive Hans-Joachim Watzke said that he expected Sancho to travel to Bad Ragaz in Switzerland for the pre-season training camp and subsequently stay at the club.
"I assume that Jadon will go to training camp on Monday and play with us for the coming season," he said last Wednesday.
The 20-year-old has two years remaining on his Dortmund contract – having joined from Manchester City in 2017 – and is eager to return to English football by joining United.