Manchester United midfielder Paul Pogba is a doubt for the visit of Arsenal on Monday because of a swollen ankle suffered in the Carabao Cup win over Rochdale in midweek.
The Frenchman was back in action for the first time since injuring his ankle at Southampton last month and completed 90 minutes in the third-round clash against their League One opponents at Old Trafford on Wednesday.
Pogba did not take a penalty in the shootout victory and did not attend a team bonding dinner following the fixture, but Solskjaer attempted to squash any scrutiny by revealing the 26-year-old's ankle had flared up again.
The Norwegian said: "The situation is he finished the game, which is fantastic but he got a knock to his ankle which is very swollen.
"It was better for him not to go there (to the dinner) with the team and he's in a race, I would guess, for Monday."
As for the availability of Anthony Martial and Marcus Rashford, who are struggling with thigh and groin complaints respectively, Solskjaer added: "I wouldn't put my life on it, no.
"That's part of this game, you work with what you have."
Solskjaer believes having a number of his forward-thinking players sidelined in recent weeks can be attributed to their lack of goals.
While they opened their Premier League campaign with a 4-0 trouncing of Chelsea, United have scored on only four more occasions in five matches since then.
Solskjaer said: "Going forward that's where we've struggled with injuries; Paul, Anthony, Marcus, we've had some bad luck in that respect.
"It's about building relationships and that doesn't help when you lose players because these boys need to get their patterns of play, work with it and get used to it.
"If you're half a second earlier in your movement, it's so much easier.
Ole on Mason Greenwood: "Against Astana and Rochdale, he's shown when you get him in the box he's dangerous. When you're not 18 yet and you keep trusting yourself, he gets the chances, so I'm not worried about him at all." #MUFC pic.twitter.com/o4Jj31I98L — Manchester United (@ManUtd) September 27, 2019
"Sometimes the finishing could have been better, it's frustrating when you've got massive chances and you don't take them. But that's also down to some outstanding keepers out there."
The likely absences of Martial and Rashford could open the door for teenager Mason Greenwood, who scored the winner in the Europa League win over Astana last week while he broke the deadlock against Rochdale.
Greenwood made his first league start in the final game of last season against Cardiff and has been a regular on the bench in the top-flight in this campaign.
Asked whether the 17-year-old is in contention to start up front against the Gunners, Solskjaer said: "He might be.
Important win to get us up and running. Refocus now for the weekend 🔴⚪️ pic.twitter.com/t2bDVeRbFf — Marcus Rashford (@MarcusRashford) September 19, 2019
"He's proven when he has been on the pitch in the last two games he's started against Astana and Rochdale, when you get him in the box he's dangerous.
"What's pleased me about him in the period that we're in is he doesn't turn down chances to finish. When you're not 18 yet and keep trusting yourself, he gets the chances. I'm not worried about him at all.
"We've managed him. We can't just throw him in at the deep end all the time so he's proved in those games he's ready for it. I'll have the weekend to think about it."
There was better news on the injury front for full-back Luke Shaw, who is set to return to training on Friday after a month out with a hamstring problem and will be assessed ahead of Monday.
Solskjaer added: "He's getting there. Let's see how he reacts to the next couple of days, he's been working really hard.
"We hope to see him before the international break, maybe Monday. I'm not too sure but maybe."
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