When asked if Rashford and Martial will feature against the Gunners, Solskjaer said: “I wouldn’t put my life on it.”
But he will consider giving a third start in 11 days to teenage striker Mason Greenwood despite being mindful of overloading a young talent.
“He might be (in contention) because he has proven when he has been on the pitch,” he added.
“When you get him in the box he is dangerous. What has please me is he doesn’t turn down chances to finish.
“He has proved he is ready for the Premier League but I have the weekend to think about it.
“We have managed him so far and we can’t just throw him in all the time.”
United have had a hit and miss start to the season.
The Red Devils have already lost at home to Crystal Palace in the Premier League, as well as just edging past Rochdale in the Carabao Cup.
And Solskjaer says his side are progressing well and you can see improvements.
He said: “In my own words: it’s a team improving, evolving, a young team, the culture is there I see them every single day in training and we don’t have any issues with attitudes, with work rate, with desire.
“Now can we trust ourselves, you can see against Astana and Rochdale they want to impress, do well and maybe they rush their finish at times.
“It is getting there.”