Pogba has been repeatedly linked with a move to Real after he hinted that it may be time for a new challenge in his career two months ago.
However, Solskjaer insists the star midfielder is going nowhere after United’s 1-1 draw with Southampton at St Mary’s.
The Manchester United manager said: “Paul Pogba will be playing for us.”
Solskjaer, though, did have some bad news regarding Pogba as he confirmed that he twisted his ankle during the match.
The Norwegian gaffer hopes it is nothing serious and that he will be able to play for France in the Euro qualifiers against Albania and Andorra.
Solskjaer added: “He twisted his ankle, I think, but he’ll go away and hopefully it’s not too bad and he can play for France because I know how much he loves his country and playing for them.”
Pogba powered through his ankle injury and played the entire match, which saw the Red Devils pick up the lead through Daniel James before Jannik Vestergaard’s equaliser.
Solskjaer admitted that United put together a sloppy performance but pointed out that the France international was a major creative force in the last half hour of the game.
He said: “I think we as a team after about half-an-hour started giving sloppy balls away and Paul was one of them.
“He wasn’t any different to anyone else.
“We as a team didn’t play well but in the last 20 minutes or half-an-hour he did create loads for us going forward.
“Everyone expects everything from him every game, he has to defend, he has to attack, he has to win headers, he has to dribble past people, he has to make passes.
“That’s just Paul and he’ll thrive on that.
“And he got a bad knock on his ankle.”