Pogba has only won two major trophies since arriving at Old Trafford, picking up the League Cup and the Europa League during his first campaign in 2016-17 under Jose Mourinho.
But he has since struggled to settle within the first team at United and it has led to his agent Mino Raiola claiming he will leave the club in the near future.
Solskjaer though believes the midfielder can still play a role at United and that the France midfielder can be prevented from leaving the Red Devils for a second time if the club start to challenge for major honours on a more regular basis.
‘It’s always a demand here at Manchester United to win trophies,’ Solskjaer told ESPN. ‘And the more we win trophies, the more players will want to play for us – then the higher standard you’ve got to set yourself.
‘It’s a demand for the players, a challenge for the players that we want them to improve and get better and better.
‘Paul has been here now for a while and, of course, he wants to win more trophies. He’s got a very, very good attitude to training and playing football.
‘He loves football, he’s ambitious, he wants to have success – like most of the others that are in the squad. We’re not all the same.
‘I would say that this squad has impressed me with their attitude and spirit lately and the way that they go about their work.
‘Of course, it’s down to us to win trophies and then we’ll see who will be part of the team going forward.’
United are back in action on Wednesday night as they look to reach the semi-finals of the League Cup when they visit Everton.
Last season, Solskjaer’s side reached the last four in the competition as well as the FA Cup and the Europa League but failed to win any of them as they ended the season without a trophy.
The United manager believes his team have grown stronger mentally though from the experience and has challenged his side to now go on and start reaching finals.
‘We were disappointed that we didn’t get to a final or lift a trophy [last season], but that’s the next step for these players now,’ Solskjaer added.
‘I think everyone felt how close we were and the mood, the spirit and the culture has improved since then. And the belief. Definitely the belief has grown.’