The Borussia Dortmund winger has been heavily linked with a move to Old Trafford this summer, with manager Ole Gunnar Solskjaer prioritising a move for the 20-year-old.
After Odion Ighalo extended his loan stay to January 2021 on Monday, Solskjaer now feels he has sufficient depth up top and can direct all of his attention towards Sancho, although United remain unwilling to match Dortmund's £100million valuation.
Sancho - who was so impressive prior to football's shutdown due to the coronavirus pandemic - has picked up where he left off, scoring a hat-trick on Sunday against Paderborn, his 17th goal - alongside 16 assists - in 27 Bundesliga games this season.
And Brown believes Sancho is exactly the type of player Solskjaer and United need.
Of what qualities Sancho would bring, Brown 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."