Stam, who represented the Red Devils between 1998 and 2001, has said that the England international would have a "big influence" if he made the move to Old Trafford.
"At United, Sancho gets an opportunity to play and he can be a real influence and help them out," Stam told 888sport. "It's one of the biggest clubs in the world and players look at the future and how a team is trying to play.
"They want to talk to the manager as well about the prospects of the club. Probably every club will tell him the same story. But when you look at him and what he can do he can be a real big influence at United should he go there."
Sancho is enjoying another impressive campaign for Dortmund, scoring 16 times and registering 17 assists in 31 appearances in all competitions for the German giants.