The Hammers are suffering an injury crisis at the moment, with no fewer than six players on the treatment table, and Allardyce admits that it is a concern.
"It's particularly worrying at the moment," he said. "James Collins, Winston Reid, Guy Demel, Diego Poyet, Doneil Henry and Andy Carroll lie in our medical room at the moment.
"We're not sure how many of those will make it for Sunday. With such a big week coming, three games in a week, there'll be very few risks taken, unless they're 100% fit. If we play them it may exacerbate the injuries so we will go to battle with what we've got."
The Hammers had to put out a makeshift defence in their last fixture against Liverpool, which they lost 2-0, and they will be hoping that a similar result doesn't ensue this weekend.
Allardyce's men have looked short of the form which made them such a force at the start of the season of late, but they take on Manchester United confident of picking up a result.
United may be in contention for a top-four place, but they have certainly not played to their maximum potential and the Hammers will know they have a chance of beating them should they turn in a good display.
The London outfit have already toppled Liverpool and Manchester City at the Boleyn Ground this season and they will be hoping to add another memorable victory on Sunday.