It comes after Borussia Dortmund's reluctance to budge from their £110m asking price.
The Bundesliga outfit are confident over their pricing because of the fact Sancho still has three years on his contract.
The England international, unlike previous players such as Ousmane Dembele and Robert Lewandowski, is not actively pushing for a move away.
United have been left frustrated by Dortmund all summer through their attempts to negotiate a deal.
The Signal Iduna Park side have insisted on using intermediaries to engage in talks on their behalf instead of direct contact.
It has left United chiefs baffled, who have had to spend potentially unnecessary money on agents and more.
And ultimately, it has been for nothing with Dortmund refusing to budge over their asking price.
According to ESPN, it has left the Red Devils feeling as if a deal cannot be made as a result of their unrealistic ambitions.
The Old Trafford outfit have been working on a transfer for Sancho throughout their Donny van de Beek pursuit.
The Netherlands international has become the first signing of the summer for Solskjaer.
Ed Woodward is prepared to make a deal worth a number of structured payments to Dortmund over Sancho.
But ESPN report that he is also happy to walk away from a deal if an agreement cannot be reached.
Furthermore, United have other targets in mind should they decide to abandon their pursuit of the 20-year-old.
The Frenchman scored the winner against Paris St-Germain in the Champions League final but could be sidelined with the arrival of Leroy Sane.
Meanwhile, Solskjaer has urged United chiefs to act smart in the transfer window and sign the right characters.
“We've come quite the distance since February,” Solskjaer said. “But you saw how tired you were towards the end. We need the break.
“It's going to be a strange summer. The market is open for so long. We've got to be good, smart and clever.
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“We're looking at it. I can't say when and if they're going to be done. It's a quick turnaround. We have to be 100 per cent sure when we make those deals.
“We definitely need to improve if we want to move up the table and on in the cups. We are working to improve what we have. We're always looking to improve the squad.
“It's not about marquee signings, it's about quality. You need the right personality to make us better. We might look at it today and see where we need to improve. Maybe today showed that they have to learn and get the consistency.”