The Frenchman has come under fire this season for his performances in the middle of the park, in particular his relaxed attitude on the ball in dangerous areas.
Fletcher, who spent 12 years at United, explained in Pogbas days playing in the reserve side, the United coaching staff and Sir Alex Fergyson agreed he could not organise a midfield.
The first time I spent out with my illness I did a spell coaching the reserve team when it included Pogba, (Jesse) Lingard, (Ravel) Morrison and we played him higher up the pitch in attacking areas, Fletcher said on Sky Sports.
We felt like he was the one who would win us game, coupled with the fact he was ill-disciplined in the middle of the park.
Sir Alex Ferguson probably felt the same. It goes back to a famous game where we feel he left Manchester United off the back of it.
We lost to Blackburn 3-2 and all our midfield players were injured. The manager picked Ji-sung Park, Phil Jones and Rafael da Silva and Paul was on the bench.
At that time we didnt feel like he was disciplined enough for the reserve team to be playing in the middle of the park so to then jump to be playing in the first team in an important game was a big step.
Mourinho has hit out at Pogba through-out the last 12 months, as the World Cup winner has struggled for consistency.
But Fletcher thinks Pogba needs to be let off the leash, and urged Mourinho to play his star man further forward.
I like to see him in the final third and creating things, Fletcher said.
He played for Juventus [on the left] and I spoke before about his connection with [Anthony] Martial. Pogba can easily drift out wide.
He can also get in the box, hes a big lad. Id love to see him with a bit more freedom to express himself.