The Red Devils have been chasing the England international all summer after Ole Gunnar Solskjaer made him a priority.
Sancho had a fine campaign last season, scoring 17 and assisting as many in the Bundesliga.
But Borussia Dortmund have told United they must stump up the £108m asking price or do not bother.
That has been a figure out of their reach – though they have not given up.
With less than two weeks left in the transfer window, United remain optimistic that the 20-year-old will be at Old Trafford by the end of it.
But with such large finances involved, pulling off such an audacious deal remains to be seen.
His arrival would appease United fans but Liverpool legend Carragher reckons the Red Devils should call off the pursuit.
Manchester United are looking to plot their path back to the top. Ole Gunnar Solskjaer has already brought in Donny van de Beek but Jadon Sancho remains Manchester United’s number one target.
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With Mason Greenwood coming up through the ranks, Carra reckons United should continue his development.
He said: “United’s hesitation in meeting Sancho’s valuation so far in this transfer window feels like it is an attempt to reverse the culture of overpaying.
“As fine a player as Sancho is, is he worth £108 million?
“And what impact would such a deal have on the game time of Mason Greenwood, who looks like the best young attacking talent in the country by some distance, scoring 17 goals last season?
“If United think Sancho is worth it, the deal should have been done already.
“What I cannot understand is if United do not think so, why haven’t they moved on?
“If the deal is not right, regardless of how much it upsets fans, walking away and buying an alternative target can be a sign of strength, not weakness.”
United have made just one signing this summer in the shape of Donny van de Beek but there remains confidence that more deals will be done.
And that could be with or without Sancho, as a move for Porto star Alex Telles remains in the pipeline.