Neither Martial nor Lingard made it to the second half against PSG and were expected to miss between two and three weeks of action as a result. Yet both appear to be recovering ahead of schedule and now at least have a chance of featuring 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 MUTV on Friday morning, still two days ahead of the game.
"So maybe more hope than think, with Anthony as well, but he's got a chance Anyway, we still hope Jesse could be ready," the boss added.
"Let's see. We've still got a couple of days' training left and they need to be part of it."
The return of either or both players would be a huge boost to United's hopes of beating Liverpool. Such a result would further strengthen United's own position within the Premier League top four as well as dent Liverpool's title ambitions.
"I've played a few of these myself so I know the magnitude of it for the fans and for everyone that works here. We have to stay focused and controlled, but have some fight in us as well," Solskjaer later said of Sunday's game as he spoke at his weekly press conference.
Ole on facing Liverpool: "I've played a few of these myself so I know the magnitude of it for the fans and for everyone that works here. We have to stay focused and controlled, but have some fight in us as well." #MUFC— Manchester United (@ManUtd) February 22, 2019
"We have to perform better than we did against PSG. That's the focus because it's a big game against a big team. We've got to learn from that experience and make sure we stay focused the whole game," he added.