The former Arsenal man believes Louis Van Gaal will have to improve his side in several areas, but two are key.
Manager Louis Van Gaal is expected to invest heavily over the summer as the Red Devils look to freshen up their squad ahead of a return to Champions League competition.
They also spent £150 million last season on attacking talents such as Angel Di Maria, Radamel Falcao and Ander Herrera, while the likes of Luke Shaw and Marcos Rojo were brought in as defensive reinforcements.
And it is in defence where Wright believes they will have to strengthen again, with central defence a key area in need of improvement.
“I think they need two centre halves without a shadow of a doubt,” he said.
“I’m not sure Phil Jones and (Chris) Smalling are going to be able to play at the level that Manchester United are going to kick on to, to actually win the Premier League. I think they need another forward, I don’t know what’s going on with Robin Van Persie.”
The Red Devils have endured an up and down campaign under Dutchman Van Gaal, having initially struggled at the beginning of the season as he failed to settle upon a formation and line-up that suited him.
They rallied in the second half of the campaign, though, with impressive wins over Manchester City, Liverpool, Tottenham Hotspur and Aston Villa all raising expectations for next season.
That fine run through to the end of the 2014/15 season saw them return to the Champions League at the first time of asking, but Wright questions whether it was the lack of proper competition, rather than United’s quality, which saw them finish in the Premier League's top four.
“I still look at Manchester United and think, okay they finished in the top four but it’s because the other teams are not as good,” he added.