Solskjaer said: "Maybe the future might have been worrying him and that's part of the reason he's injured".
"Who knows? Hopefully he can be available for Chelsea or [Manchester] City but I'm not sure".
"He's been working really hard to get fit from his injury he sustained against Liverpool, then he came back and got a different one here in training".
He has failed to score in his last eight appearances, but Solskjaer said he was happy with the midfielder's contribution, particularly during the Champions League home defeat to Barcelona on Wednesday.
Diogo Dalot would be the obvious choice at right-back, unless Solskjaer continues to play the Portuguese youngster further forward.
'We'll see who's here for next season and I've got a couple of players in my head that could be captain, ' Solskjaer admitted on Friday.
Asked about his squad, Solskjaer added: "It's going to be survival of the fittest or survival of the best".
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While Pogba was not able to provide a cutting edge, Solskjaer has praised his work rate and contribution to the team. I think now you are going to have to see the real Man United players come up.
"There aren't many games left", Rojo said.
Ole Gunnar Solskjaer's side are in sixth place in the table and five points adrift of third-placed Chelsea FC in the race to secure one of the final two Champions League spots.
Zinedine Zidane's return to the Bernabeu helm has fuelled talk, while the wheels appear to be in motion with the kind of campaign often associated with the Champions League holders when they target a player.
"I don't know how they've been the last few talks, but we've let him focus on his fitness as well".
"But now it's about West Ham and focusing on a good performance to give us three points". Not too many as we've lost Luke and Ashley through suspension.