The England forward scored United's only goal of the game against Paris Saint-Germain before having to withdraw due to injury.
Solskjaer confirmed afterwards that he was substituted due to a "niggling" shoulder injury, and that the club hoped Rashford would be available for the match versus West Ham.
Although he could still feature, it might be an opportunity to save him for next week's massive Champions League clash against RB Leipzig.
Should Rashford be left out, or start on the bench, expect a straight swap with Mason Greenwood.
Edinson Cavani still awaits news on a potential ban for alleged racist comments on a social media post after the Southampton game, but if available he'll start, having emerged as the match winner against the Saints.
David de Gea had to be withdrawn due to a knee injury in the game versus Southampton, but did return between the sticks for the PSG game so should be fine to feature again.
With Luke Shaw not close to full fitness after injury, Alex Telles should feature at left-back alongside the usual trio of Harry Maguire, Victor Lindelof, and Aaron Wan-Bissaka in the back four.
Fred's ridiculous red card against PSG could see him punished with a place on the bench, with Nemanja Matic coming in.