The former Red Devils defender has heaped praise on the England international - who has been link with a move away from Borussia Dortmund - and insisted he would be a perfect fit for the club.
Asked what Sancho would bring to Old Trafford, he told MUTV: "Talent and excitement...
"We need someone exactly like that at the club. We've had them over the years and I'm sure if we were to sign him he would bring that excitement back to the club. It would be good for the team as well.
"We've had players like that in the past, like with Cristiano Ronaldo. They're the type of player who draw three or four defenders out and make the game a lot easier for the other players.
"If we could do it, it would be a brilliant signing."
Brown's sentiments were echoed by former United man Danny Webber, who insisted the team should make the 20-year-old star their "number one target".
He added: "I think Sancho would be the number one target. He ticks every box.
"He's exciting and has the courage to get on the ball. He's already got that end product so for me he would be the number one target this summer."