The West Ham boss was unable to bring in any defenders on loan in the closing days of the winter transfer window and injuries have left him with very few options when Louis van Gaal's side arrive at Upton Park.
Winston Reid and James Collins are both absentees and Allardyce is likely to ask fit-again Senegalese midfielder Cheikhou Kouyate to step into the defence and partner James Tomkins, himself only just back from injury.
With club-record signing Andy Carroll struggling for fitness after suffering an ankle problem at Liverpool last week, the Hammers are light on numbers as they go in search of just their second Premier League win of 2015.
"(The injury list) is particularly worrying at the moment," said Allardyce.
"I've had to bring a list of the injuries with me
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 per cent fit
If we play them it may exacerbate the injuries so we will go to battle with what we've got.
"It is why we went all out for a defender in the window after the Liverpool game
However it didn't work out, we were only in a position to get someone in on a loan but we couldn't pull it off.
"Everyone that wanted to come wanted a permanent deal, which we couldn't do at that time, so that's the position we're in
Someone will have to fill in at the back and maybe stay there for a while."
Carlton Cole will be in the squad after his proposed move to West Brom was cancelled late on
The striker could yet lead the line with Carroll doubtful and Diafra Sakho's position in the side still in doubt following the fine handed down by FIFA for West Ham's breaching of the regulations
Sakho came off the bench to score in the 1-0 FA Cup win over Bristol City despite the fact he had not travelled to link up with Senegal at the African Nations Cup due to a back injury.
West Ham, who maintain they did not break any rules, blocked any questions on Sakho's situation at Allardyce's pre-match press conference and the former Bolton boss was bullish when asked if his top goalscorer could play against United, answering simply: "We will see."
Former Hammers midfielder Michael Carrick remains United's only injury concern.
The 33-year-old has not played since the FA Cup fourth-round trip to Cambridge a fortnight ago due to a calf strain.
Defender Jonny Evans and winger Ashley Young returned to action after injuries in Tuesday's replay victory over Cambridge at Old Trafford.
United are third in the league and boss Van Gaal wants to push on to enjoy a strong second half of the season.
Trailing leaders Chelsea by 10 points, he does not realistically believe they can become a factor in the title race - but he is not ruling it out.
He said: "It should be fantastic, of course, for the fans - but our goal is ending in the first four of the league and winning the FA Cup.
"There are still 16 clubs who want that, so that shall be difficult and ending in the first four is also difficult because there are teams breathing down our necks.
"It shall be very difficult to catch Chelsea, but it is mathematically possible
So we shall try to do everything we can to win every game
We are capable of doing that.
"It is possible, but it is also difficult
If I had to bet, I would bet on Chelsea - but I am not allowed to bet."
Source : PA
Source: PA