United finished sixth in the top-flight last term, a hefty 24 points adrift of champions Chelsea.
Ex-United defender Irwin expects Jose Mourinho’s side to be in the mix for this season’s crown and believe Pogba can be the driving force in their title tilt.
Irwin said: "I expect Paul Pogba to be a really powerful player this year.
"I expect Manchester United to challenge for the title. More consistency is needed.
"We drew too many [last season] and I think more goals are needed from different areas.
"Last season there was an over-reliance on Zlatan. Rashford, I think, will score more goals."
As for United's new signings, Irwin thinks it has been a summer of good business in a transfer window of ‘eye-opening’ amounts spent on players.
Victor Lindelof, Romelu Lukaku and Nemanja Matic have all been snapped up by Mourinho.
Irwin said: "Lindelof will take a bit of time but will turn into a very good player.
"Lukaku and Matic are good additions. Matic is a really experienced, solid performer."
Irwin does admit, however, that United will have a fight on their hands if they are to claim Premier League glory.
He said: “Chelsea have got European football and Spurs are now at Wembley.
"Manchester City will be strong this year and Arsenal have bought a striker which was needed.
“I wouldn't dismiss Everton. It's going to be a very competitive league I think."