He is, however, now a World Cup winner and a man handed the United armband despite reports of a breakdown in his relationship with Mourinho.
Scholes believes Old Trafford remains the best place for the 25-year-old, with it difficult to see how he would fit into a system at Camp Nou.
The Red Devils legend told Radio 5 Live: "I just don't see Pogba as a Barcelona type player. We hope he stays, every team wants to keep their best players and we want him to stay.
"He has amazing qualities but has not shown them enough. Hopefully he can drive United to a title challenge."
Scholes added on reports of a row with Mourinho, which the Portuguese has played down: “I don't know - there’s obviously some sort of breakdown in their relationship from what we read.. do we know that for definite? I don’t know.
“What we do know is that Paul needs to perform more often than he is doing.
“We all know the talent that he’s got. Great ability, great strength, an athlete, but he’s only doing it once every three of four games and if you’re going to challenge for a title I just don’t think that’s enough.”
Pogba silenced some of his critics with a goal-scoring display in United’s opening Premier League fixture of 2018-19 against Leicester.
That was his first outing since the World Cup final, with Scholes hoping to see the midfielder handed more responsibility over the coming weeks as a leadership role appears to bring the best out of him.
The ex-England international said: “Course he showed desire [against Leicester], he should be showing that every week anyway. Captain's armband? I thought the minute we signed him he should have been made captain.
“Give him some responsibility, a young player. I don’t think there was a standout person to be captain in that team, I just that that was ideal for him hopefully he can keep that.
“He started okay Friday, I don’t think it was anything special. If he can thrive on the responsibility then yes, keep him with the armband.”