The former Red Devils defender admits the England international would be a welcome addition at Old Trafford, with a summer move being mooted
Ole Gunnar Solskjaer is said to have the England international in his sights heading towards the summer transfer window.
United are not the only side weighing up the merits of launching a raid on Dortmund for the talented teenager.
They are, however, prepared to invest heavily in the youngster’s potential if an exit door is opened in Germany and interest in a return to Manchester is displayed by a former City academy star.
Stam hopes the Red Devils will be in the mix, with the 1999 Treble winner of the opinion that a more direct threat on the flanks would aid the cause considerably at Old Trafford.
He told 888sport: “At United, Sancho gets an opportunity to play and he can be a real influence and help them out.
“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.”
United already have plenty of firepower on their books, but inconsistency has proved to be a problem once again in 2019-20.
France international forward Anthony Martial slips into that category, with the 24-year-old recording his 13th goal of the season in a 2-0 victory over Chelsea but still facing questions of his value.
Stam added on the need to keep faith with players who still have plenty to offer: “He scored a very good header against Chelsea and the boy has a lot of potential. He’s got a very good personality and quality on the ball. And he has pace.
“Sometimes he needs to play it a little more simple, instead of wanting to show his qualities on the ball and being tricky. Sometimes you need to be more direct in the way you play in order to produce.
“He still needs to do better but this is normal for a young player where sometimes you look very promising and then other times you’re not producing.
“In a big team if you want to be a big player you have to be consistent in what you’re doing. I think that’s what he’s looking for as well.”