The Hammers are four points above the relegation zone following a mixed run of form, while Norwich are 10 points from safety with four games to play.
Last week's impressive 3-2 win over London rivals Chelsea, secured through a late strike from Andriy Yarmalenko, was supposed to have kickstarted West Ham's campaign.
However, a 2-2 draw against Newcastle United four days later was a case of an opportunity lost, with United twice squandering a lead against opponents with little left to play for.
Then came Wednesday's 1-0 home loss to Burnley - Jay Rodriguez's fine header shortly before half time condemning the Hammers to a fourth defeat in six matches.
Thankfully for United, the teams below them have also struggled to pick up points since last month's restart, so there is still a four-point buffer on Aston Villa.
The Villans, as well as Bournemouth who are also on 27 points, have games in hand to play against Manchester United and Tottenham Hotspur respectively on Thursday.
United have Norwich, Watford and Aston Villa to face in their four remaining games - three of only four teams currently below them in the table - plus a trip to in-form Man Utd.
It is now effectively a battle between four teams for the two remaining relegation spots given that Norwich have already accepted their fate.
The Canaries are rock bottom of the division, as they have been since pre-Christmas, and need to win all four of their remaining matches to have any realistic hope of staying up.
With trips to Chelsea and Manchester City still to come, it is fair to say that Championship football will be returning to Carrow Road next season.
Daniel Farke's men are now playing for pride, and this visit of West Ham does at least offer them a chance to register just a sixth victory of a disappointing campaign.
Four of those wins have come at home, giving City the worst home record in the top flight.
Norwich City's Premier League form: LLLLLL
Norwich City's form (all competitions): LLLLLL
West Ham's Premier League form: LLLWDL
Star man Todd Cantwell, who looks destined to stay in the Premier League next season regardless of City's fate, missed the 2-1 defeat to Watford and remains a big injury doubt.
Onel Hernandez registered an assist at Vicarage Road and is expected to retain his place out wide should Farke stick with a 4-2-3-1 system.
West Ham welcomed record signing Sebastien Haller back from injury for the final half an hour of their midweek loss to Burnley.
The striker is now in contention to return to the starting lineup here, though Michail Antonio has performed well through the middle in recent games.
Norwich City possible starting lineup:
Krul; Aarons, Klose, Godfrey, Lewis; Vrancic, McLean; Buendia, Stiepermann, Hernandez; Pukki
West Ham United possible starting lineup:
Fabianski; Fredericks, Diop, Ogbonna, Cresswell; Soucek, Rice, Noble; Yarmolenko, Antonio, Bowen
We say: Norwich City 0-1 West Ham United
Norwich have lost all six matches in all competitions since football returned last month, losing those games by an aggregate 13-2 scoreline. West Ham can take another step towards survival with victory against the doomed Canaries, and we are tipping them to edge this weekend's clash in Norfolk.