Martial, who signed a new five-year contract at United on Thursday, missed Tuesday's 2-2 draw with Burnley after picking up a slight injury in training.
Pogba, meanwhile, was spotted limping on his way out of Old Trafford after United's last outing.
Solskjaer, however, is hopeful that both will be involved at the King Power Stadium.
"We've not had a proper session since the game," Solskjaer said on Friday. "I don't think there's anything with Paul.
"Anthony has done some rehab work, we'll try a session today. I imagine he'll be available."
Solskjaer said that Martial's new contract until 2024 shows that both he and the club have faith in the France international to fulfill his potential.
"It's confirmation that we're happy with him. We believe in him," Solskjaer said. "He's got fantastic potential. He's had ups and downs at the club. He's been developing.
"As a young lad, moving abroad it's not easy, but now he knows he will stay here for the future. I certainly believe in him."
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies