The London club have been desperate to pull out of a slump that has brought only one win in 11 games since the middle of January, leading to speculation about whether the experienced Allardyce will be offered a new contract.
He admitted last week that if they had started the season like they are finishing it, he would already have been sacked.
His team were in fourth place at Christmas, with City one of their victims in a 2-1 success at Upton Park in October.
Senegalese striker Diafra Sakho scored the winning goal that day, becoming the first West Ham player to find the net in six successive Premier League games.
But Sakho now has a thigh problem and Andy Carroll, after returning from injury during that successful spell, is out for the rest of the season following knee surgery.
"It leaves us short in goalscoring options because Andy and Sakho are our two leading scorers this season," Allardyce told a news conference.
Ecuador's Enner Valencia is fit, however, and Carlton Cole will play.
From sitting in the Champions League places, West Ham have dropped to ninth and the manager said their aim now was to reach 50 points and finish higher than in the two previous seasons since winning promotion back to the Premier League.
Allardyce is among those surprised that Sunday's opponents City are in such poor form, having lost four games out of six and dropped out of contention to retain their title.
"It's a huge shock, based on the huge amount of talent they have but like ourselves they can't find a way to win at the moment," he said.
"It'll test their nerve a little bit but, hopefully, we can test their nerve."
(Reporting by Steve Tongue, editing by Ed Osmond)
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