Both teams are level on 25 points, though the Hammers are unbeaten in three and have not conceded in the process, while the Canaries have not won at the Boleyn Ground since 1989
Allardyce's side have the opportunity to win three consecutive Premier League games for the first time since May 2007 as they bid to put some breathing space between themselves and the relegation zone.
They have recorded back-to-back 2-0 victories against Swansea City and Aston Villa, but still remain two points clear of the bottom three on 25 points, the same amount as the Canaries.
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Allardyce is now keen to record a fourth home league win of the season to help their fight against the drop.
"Ten points out of the last five games is a pretty good spell at the moment," he said after Saturday's victory over Villa.
"While we are out of the bottom three, we are not satisfied because we have only got 25 points from 25 games and we need more points than games on the board as quick as we can."
Norwich will also come into the clash in good spirits after becoming only the fourth team this season to stop Manchester City from scoring in the league.
They held on bravely to claim a 0-0 draw on Saturday, although Upton Park has traditionally not been a happy hunting ground for them.
The Canaries have not won there since March 1989 and given that they have only won twice on their travels in the league this season, ending that record could prove difficult.
They have conceded 26 goals in away matches this term, while West Ham have not conceded in their last three Premier League matches.
Top scorer Gary Hooper has not scored in his last seven matches for Norwich, but Hughton is confident that he will be fit to lead the line after being withdrawn midway through the second half against Manchester City after taking a knock.
"I think he's okay," Hughton said. "I was taking Gary off anyway, he was working really hard and we needed some fresh legs in that forward area."
Hughton will also hope to have Robert Snodgrass (groin) and Jonas Gutierrez (calf) back to supply him after they both missed the draw with City.
Andy Carroll serves the second of his three-match suspension for the hosts, so Kevin Nolan could again start up front, unless Allardyce opts to give new signing Marco Borriello his first start.