Pogba has been a polarizing figure since returning to Manchester from Juventus and he has publicly stated his desire to take on a new challenge, with the likes of Real Madrid and Inter Milan reportedly interested in his services.
An injury-ravaged campaign has seen Pogba make just eight appearances in all competitions for Manchester United this season, but he is set to make a return to action when the Premier League resumes after returning to full fitness.
Sheringham, who won the treble with United in the 1998/1999 season, is adamant Pogba should be moved on for more committed players.
"People mention top players and captains," Sheringham told Sky Sports. "When things weren't going right in our time, Roy Keane put things right. He would drive our team on, he would dig deep and make sure we had a say in every game we played in because of his desire.
"When you look at Pogba, yes, he may be a talented boy, but does he have the same mentality? Does he really dig deep and get Manchester United out of the mire when the going gets tough? For me the answer is no.
"He gives off the wrong vibe as a Manchester United player. Yes, it's good to be cocky and arrogant at the right times, Dwight Yorke had that as well, a big smile on his face when he played. But Yorke had a desire to do the right things at the right times. You've got to have that, and I don't think Paul Pogba gives you that.
"He would be one that would need to go so that you can get someone in with the right mentality and desire to drive Manchester United out of the position they are in."
