Pogba has 18 months left on his contract and Mino Raiola, his agent, has said that the midfielder wants to leave Manchester United.
He will enter the final year of his contract at Old Trafford in the summer and the club are expected to try and sell him in order to recoup some money from his departure.
But Solskjaer indicated that Pogba’s mind about leaving Manchester United could change if the club start winning trophies and demonstrate that they can challenge for top honours.
He insisted that has no complaints about Pogba over his attitude in training and during games despite the speculation surrounding his future.
The Manchester United manager stressed that the Frenchman wants to win trophies and it is up to the club to make sure that they compete for and win the top honours.
Solskjaer told ESPN FC when asked what he can do to prove to Pogba that Manchester United are the best place to win trophies: “There’s always a demand at Man United to win trophies, and the more you win trophies, the more players are going to want to play for us.
“Then, there’s a higher standard you’ve got to set yourself.
“It’s a demand for the players; it’s a challenge for the players that we want them to improve and get better and better.
“Paul has been here for a while, and of course he wants to win more trophies.
“He’s got a very, very good attitude to the training and his football.
“He loves football and he’s ambitious.
“He wants to have success like most of the others that are in the squad.
“We’re not all the same, but I would say that this squad has impressed me with their attitude, spirit and the way they go about their work.
“It’s down to us to win trophies, and then let’s see who will be part of the team going forward.”
Pogba is in line to start against Everton in the EFL Cup quarter-final at Goodison Park tonight.