Martial has been out of action with a thigh injury since United's 2-1 defeat to Crystal Palace at home.
His versatility will be missed badly.
Rashford picked up a groin problem against West Ham last weekend.
His absence takes the shine out of United's attacking quartet to leave the side in despair.
You work with what you have, says Solskjaer
Ole said he has to work with what he has got. "I wouldn't put my life on Rashford and Martial being fit, that's part of this game - you work with what you have."
Focus on 17-year-old Mason Greenwood
United are left with one recognized striker in the form of 17-year-old Mason Greenwood.
The teenager has scored two goals so far in the Carabao Cup and Champions League respectively.
Ole is considering in playing him against Arsenal.
"He [Greenwood] has proved when he gets in the box he is dangerous," the United boss said.
"I have the weekend to think about starting him."
Luke Shaw back for United
The only positive news for United is the return of Luke Shaw in training.
He missed United's last five matches due to a hamstring problem.
"Luke Shaw is back in training today, he is getting there, so let's see how he reacts in the next couple of days," Solskjaer said.
The club will not look to rush him though on his return.
United in a spot of bother against Arsenal
United will find it difficult against Arsenal, who have won three successive games across competitions. The major issue for the hosts is the lack of quality in the final third. Also, defensively they cannot afford to give Arsenal the space to create opportunities.