Sam Allardyce's side have registered two wins and a draw from their last four games to move closer to safety, while the hosts have climbed up to 10th in the tableWest Ham will be looking to continue their encouraging form on Saturday against Aston Villa.
Captain Kevin Nolan scored both goals as the London club beat Swansea City 2-0 at Upton Park last weekend on the back of a battling goalless derby draw at Premier League title contenders Chelsea.
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Striker Carroll will now face a three-match ban after West Ham's appeal against his dismissal for a clash with Chico Flores failed.
Nolan has no doubt they can see off Villa in his absence, but the midfielder is wary of the threat posed by strike duo Christian Benteke and Gabriel Agbonlahor.
He told the club's official website: "Villa are a good team at home, they counter well and they've had good results lately. But we know we've got enough to go there and get a result.
"Paul Lambert has had to restructure the wage bill there, so he's done a good job with that. He has a lot of young players who are working hard for each other and for the team.
"Then obviously they've got Benteke up front. We need to keep him and Gabby Agbonlahor quiet and hopefully go there and get some points."
History is not on the visitors' side ahead of the trip to Villa Park, as they have not won there since January 2006.
Tenth-placed Villa have secured all three points in four of their six top-flight home games against the Upton Park outfit since then, and know another victory will leave them 10 points better off than Allardyce's men.
Leandro Bacuna's first-half strike proved to be in vain as Villa suffered a 2-1 defeat at Everton last weekend, having been in front with 16 minutes remaining.
Villa beat West Brom 4-3 in a derby thriller in their last home match, but failed to win in their previous six homes matches.
Lambert will check on the fitness of Agbonlahor (foot) and defender Ron Vlaar (hamstring).
Chris Herd (hamstring) is back in contention and fellow defender Joe Bennett (back) could also feature, but Jores Okore (knee) and Libor Kozak (broken leg) remain sidelined.
Carlton Cole and Marco Borriello will be vying for a start in the absence of Carroll, while it remains to be seen if midfielders Mohamed Diame (knee) and Joe Cole (groin) will feature, and defender Joey O'Brien (shoulder) is definitely out.
Antonio Nocerino has made two substitute appearances since his loan move from Milan and the midfielder may have to wait for his first start.