United were beaten 5-3 away to Leicester City in their last game, and Allardyce admits that he would be happy to take a point away from the North-West.
He told reporters: "They will be pretty down about that performance they gave at Leicester. I'm thinking [it will be] a backlash. I think that because of the determination of the Manchester United players and the fact they are playing at Old Trafford.
"They will be hurting and they know the only way they can put that right is to get out onto the field and punish us for it - so we will have to be careful about that.
"A draw would be great for me. Anything more than a draw would be outstanding as far as I'm concerned."
The Hammers are currently eighth in the Premier League.