His performances, however, have often been the subject of criticism at United, with a dispute between the player and Jose Mourinho, plus persistent rumours linking him with a move to Barcelona at some point in the future, overshadowing the beginning to the season.
Instead of being a staging post for the midfielder to stamp his authority on the Red Devils, the Premier League legend believes World Cup success will, instead, be a prompt for the 25-year-old that everything is going along just fine.
"In the Premier League, if we are honest, he hasn't done it consistently," Wright told ‘The Debate’ on Sky Sports.
"Coming back with the World Cup medal has given him a false sense of security and made him think he is bigger than this.
"We need to see more of him and what he is capable of doing.
"I am sure there are teams that would want him and are monitoring the situation."
Additionally, the ex-England striker suggested that being a world champion will only have inflated the player’s ego further, which is sending him on a collision course with Mourinho, particularly in light of the disappointing form of the player and the team. Furthermore, the player has failed to quell speculation that he could leave the club.
"There are two massive egos and neither are backing down,” he added.
"Pogba could have easily shut it down but Manchester United fans are thinking: ‘Here we go again'.
“I think Pogba could blast it out of the water by playing well because then Mourinho will have a problem.
“If he keeps playing as he is then Mourinho is in his rights to say he isn't getting enough.”
Pogba was involved as France drew 0-0 with Germany in the opening Nations League match of their campaign on Thursday in Munich. The world champions were stretched regularly by their hosts, but a string of fine saves from debutant Alphonse Areola kept their opponents at bay.