While United have come through a gruelling festive fixture run with an impressive run of results, Solskjaer was not keen to rest too many of his star players at Craven Cottage as his side hope to go back above Leicester at the Premier League summit.
"His form is very good," the United boss said. "He was just voted Player of the Month (for December). He's not tired, no, no chance.
"He is one of the players that runs and covers the ground in every single game, he's very good at recovering and recharging his batteries.
"If he scored his free-kick or if it just had a little air on the ball when Luke (Shaw) put the cross in he'd have been lauded as the best player in the Premier League again.
"Since he's come in, he's been absolutely immense. He's not tired and if I ask him he'll say there's absolutely no chance that he's tired."
That means Donny van de Beek is once again be a substitute, though Edinson Cavani and Mason Greewnood - both on the bench on Merseyside - start with Marcus Rashford rested.
Eric Bailly comes in for Victor Lindelof, while Fred starts in midfield alongside Paul Pogba.
Solskjaer ruled Phil Jones and Brandon Williams out of tonight’s match through injury, while the United boss suggested January acquisition Amad Diallo would not be called upon just yet.
Manchester United XI: de Gea, Wan Bissaka, Bailly, Maguire, Shaw, Pogba, Fred, Greenwood, Bruno Fernandes, Martial, Cavani
Subs: Mata, Rashford, James, Henderson, Alex Telles, Matic, van de Beek, Tuanzebe, McTominay
Manchester United squad from: De Gea, Henderson, Grant, Wan-Bissaka, Tuanzebe, Lindelof, Bailly, Maguire, Shaw, Telles, McTominay, Fred, Matic, Van De Beek, Pogba, James, Fernandes, Lingard, Greenwood, Rashford, Martial, Cavani, Ighalo.
Injury list: Phil Jones (knee), Brandon Williams (knock), Marcos Rojo (calf), Facundo Pellistri (Covid-19)