Pogba has put in a series of poor performances this season that have seen him axed by Jose Mourinho.
It’s unclear whether he will start against Liverpool on Sunday but Sutton is in no doubt about one thing – he would thrive under their boss Jurgen Klopp.
United sit 16 points behind the Reds after just 16 games of the season.
“Paul Pogba would excel under both Pep and Klopp – better than he would do under the manager now,” Sutton said while appearing on BT Sport’s Saturday Morning Savage.
Fellow pundit Tim Sherwood, appearing alongside Sutton on the show, agreed.
“I think Pogba needs to play in a philosophy that he’s used to playing in,” he added.
“We saw how brilliant he was at Juventus, he went and won the World Cup, he’s a different class.”
The show’s host Robbie Savage had earlier savaged Pogba’s boss Jose Mourinho over how Manchester United are failing.
“Why can’t Mourinho get the best out of record signing Paul Pogba? Do you seriously think Klopp or City boss Pep Guardiola would struggle to harness his talent?” he told the Mirror.
“And even if United were to part company with Mourinho, who has the stature and the personality to take on the job?
“They aren’t going to get Klopp or Guardiola, and Zinedine Zidane doesn’t seem to be in any rush to try his luck in English football.
“Mauricio Pochettino hasn’t won a trophy yet, and United would have to pay big compensation to Tottenham to get him.
“Much as it pains me to say it, Manchester United are drifting – and I’ve got no idea how it’s going to change.
“Realistically, the only trophy they can win this season is the FA Cup. And winning that wasn’t enough to save Mourinho’s predecessor Louis van Gaal.”