The Red Devils have also recruited France center half Raphael Varane.
While Carragher is impressed with Varane, he believes winger Sancho will add an extra dimension to United's team in the coming campaign.
"I actually think the acquisition of Sancho is a really good signing," the Liverpool legend told UMM.
"I think Varane has been brilliant for Real Madrid next to Ramos.
"But I actually think Sancho is a better signing for Man Utd long term."