But the two key men are potentially back in contention for this weekend's crunch clash at Old Trafford, having recovered well over the last few days.
Martial has enjoyed a strong season for the club, contributing nine goals and two assists in 20 Premier League appearances.
The Frenchman signed a new five-year contract at Old Trafford in January and he seems to be playing with a new lease of life under Solskjaer's stewardship.
Lingard has also been a fixture in the starting XI this term, enhancing his ever-growing reputation as one of England's finest young players.
Solskjaer revealed that Martial is closer to full fitness than Lingard, yet he hopes to be able to call on both men against rivals Liverpool this weekend.
"I hope and think Anthony will be ready and I hope Jesse will be ready because it's two different injuries," Solskjaer told United's official website.
"So maybe more hope than think, with Anthony as well, but he's got a chance.
"Anyway, we still hope Jesse could be ready. Let's see. We've still got a couple of days' training left and they need to be part of it."
The Red Devils bounced back from defeat against PSG with a superb display against Chelsea in the FA Cup on Monday, progressing to the quarterfinals after goals from Ander Herrera and Paul Pogba secured a 2-0 victory.