Pogba ignited speculation linking him with a move to Real Madrid last month, suggesting Real were “a dream club for any player”, although he declared at the time he was happy at Old Trafford.
Both manager Solskjaer and United’s board want their £89 million ($115 million) club-record signing to stay, although they have acknowledged that circumstances could change.
“You can’t guarantee anything in football but yes I think Paul is going to be here,” Solskjaer told reporters on Friday. “I can assure you that he is very determined to be successful at United.”
Pogba scored eight goals and provided five assists in his first 10 games following Solskjaer’s appointment but his performances have tailed off since, and it was a surprise to many observers that the French midfielder was named in the Professional Footballers’ Association’s team of the year on Thursday.
Former Manchester United midfielder Roy Keane this week described Pogba as a “big problem” for the club, suggesting that he was not committed enough to the team.
But Solskjaer said Pogba can cope with the scrutiny.
“That’s just the standards he sets, because when he’s creating chances, scoring goals, doing loads of work… that’s just media, supporters, everyone looks to Paul. ‘Could you have done better?’
“He’s done fantastic for us, he’s a human being as well and we’re all the same, we want him to do well.
“He’s a leader in that dressing room and on the pitch for us. Back to if I can guarantee, I would say ‘yes, I can guarantee’ but in life you can never (know), but he will be here as far as I’m concerned.”
Solskjaer, who won 14 of his first 17 matches after replacing Jose Mourinho, initially as caretaker manager, in December, is attempting to turn around an awful run of form, which has seen United’s players widely criticised.