The England forward was replaced by fit-again match-winner Paul Pogba at half-time during Thursday’s Europa League last-16 second-leg win over AC Milan with what manager Ole Gunnar Solskjaer described as a “twinge”.
The usually ever-present Rashford also missed the first leg against the Italians with a slight issue and there is not much optimism over his chances of featuring in the East Midlands this weekend.
Anthony Martial is also questionable with a hip problem and it remains to be seen if Edinson Cavani will play any part after a knock.
Eric Bailly and Juan Mata have also missed time of late along with long-term absentee Phil Jones, though Donny van de Beek returned to the squad at the San Siro.
"With Marcus I don't really know," Solskjaer said on Friday. "I can't say. (It is) most unlikely that he'll be fit, but I hope so. We haven't really got to the bottom of it.
"But with Edinson, he's worked really hard and he's joined in training sessions.
"Towards the end of the session he really needs to top it up and feel 100 per cent ready for the game and he hasn't really got there yet.
"It's down to him. He wants to be 100 per cent when he joins in. He doesn't want to feel (like he's) come in and look off the pace.
"Hopefully he can be ready for Sunday but I'm not sure either because after the training yesterday he felt something that he couldn't travel with us."
Solskjaer added that Pogba likely could not yet manage 90 minutes after the thigh injury that kept him out for more than a month, though he is hopeful that the Frenchman could start against Leicester as United seek to reach another semi-final.
Man United predicted lineup: Henderson; Wan-Bissaka, Maguire, Lindelof, Shaw, McTominay, Fred, Pogba, Fernandes, James, Greenwood
Injury list: Mata, Jones
Doubts: Cavani, Rashford, Martial, Bailly