Manchester United are searching for a new centre-back this summer and Maguire is on their list.
Jose Mourinho appears resigned not to land the Leicester defender, who excelled with England at the World Cup.
A move for Yerry Mina seems most likely with just four days left of the transfer window.
But former United defender Brown reckons Maguire would be the best fit at Old Trafford.
“Maguire had a fantastic tournament (for England at the World Cup) and has been really good for Leicester since joining them from Hull,” Brown said.
“He’s shown that he can play on the world stage.
“That’s the sort of player Manchester United need.
“He knows the Premier League and knows what it’s about.
“I never talk about the money side of it because if a player will strengthen your team then the transfer fee is what it is.
“I don’t talk about the money. All I care about is whether he will be good for the team and he definitely would be a great signing.”
Leicester are determined to keep hold of Maguire and hope he is still a Foxes player when they clash with United on August 10 in the Premier League.
A deal for Maguire would cost United around £50m and the Red Devils have therefore turned their attention to Barcelona gem Mina.
Barca are willing to sell the Colombian and talks got underway on Thursday.