Pogba skippered Manchester United for their trip to Leicester this evening, with Antonio Valencia absent through injury.
Former Liverpool midfielder Redknapp said the armband suited the Frenchman and reckons he can follow in the footsteps of club legends Roy Keane and Bryan Robson.
“What I like as well is he’s captain today, that’s a big thing,” Redknapp said on Sky Sports.
“You know what, the great midfield players; Robson, Keane, captains, leaders.
“He could go be that man for Manchester United, it’s a big opportunity for him.
“That captain armband looks good on him, it could fit for a few years.”
Redknapp also thinks Paul Pogba can adopt a similar style of play to the likes of Keane and Paul Scholes going forward in his United career.
“Get them playing, that’s the most important thing,” he added.
“Any midfield player at Manchester United it’s fundamental when you look back, and I don’t like to look back at history of clubs, but they had Keane, they had Scholes, players that can dictate the game, dictate the pace of the game, even Michael Carrick now.
“When he doesn’t play they haven’t really guy that can slide passes in with a bit of pace.
“I think when they play with (Ander) Herrera and (Nemanja) Matic they’re too similar.
“He offers something different but there is the other side of it that when he plays, he also vacates the midfield and that’s an area Leicester will look to get in behind him.
“But in terms of his ability he’s a phenomenal player, without a doubt.”