The Hammers head into the first leg of the last-16 tie sitting in 16th position in the Premier League table, while Larnaca are currently two points off top spot in the Cypriot equivalent.
Match preview
For a number of weeks, David Moyes has faced fierce pressure to retain his position as West Ham manager, a consequence of his side failing to move away from the Premier League relegation zone for much of the season.
However, despite a 4-0 defeat at the hands of Brighton & Hove Albion at the weekend, reports suggested that the Hammers hierarchy have no intention of parting ways with the Scot.
While survival in the top flight is the priority, West Ham will not shy away from throwing everything at winning this competition, for both the glory and a spot in next season's Europa League.
With European qualification realistically not possible through the league, the short-term trajectory of the club is effectively on the line in continental action.
Nevertheless, Moyes will be confident of victory on Thursday evening with West Ham having impressively won each of their eight European matches during 2022-23.
As far as Larnaca are concerned, they have already broken new ground in reaching this stage of a European competition, albeit through demotion from the Europa League.
There is an argument that was a blessing in disguise, however, with the Cypriot outfit being presented with a more realistic chance of progression versus Dnipro-1 than a higher-profile team in the competition that they exited.
Larnaca were no strangers to Dnipro-1 having played them in the Europa League qualifiers, and a late goal in the home first leg proved enough to come through 1-0 on aggregate.
Despite that success, it should be noted that Larnaca have won just two of their eight European games from September onwards, while they have collected just four points from as many matches in the Cypriot top tier since February 10.
AEK Larnaca Europa Conference League form:
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West Ham United Europa Conference League form:
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West Ham United form (all competitions):
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Team News
Larnaca boss Jose Luis Oltra will be forced into two changes with Angel Garcia and Pere Pons both serving bans for three yellow cards.
Nicolas Englezou is in line to deputise at left-back, while Rafail Mamas may get the nod in central midfield.
Oltra must decide whether to stick with the 4-4-2 formation which earned victory over Enosis Neon Paralimniou last time out, or revert to a more defensive-minded formation.
Moyes will rotate his West Ham XI with Aaron Cresswell, Pablo Fornals and Gianluca Scamacca all likely to be recalled.
Kurt Zouma will be assessed after coming through 21 minutes as a substitute at the weekend after a six-week layoff, while Flynn Downes could add fresh legs to the midfield.
AEK Larnaca possible starting lineup:
Piric; Rosales, Milicevic, Gonzalez, Englezou; Faraj, Ledes, Mamas, Jakolis; Trickovski, Lopes
West Ham United possible starting lineup:
Areola; Johnson, Aguerd, Ogbonna, Cresswell; Downes, Rice; Bowen, Fornals, Benrahma; Scamacca
We say: AEK Larnaca 1-3 West Ham United
On some level, Moyes will feel that this is one of the most important matches of his reign, the pressure on his players to deliver when his job is at risk. However, the Hammers should have too much firepower for one of the minnows remaining in this competition, potentially laying the foundations for a comfortable second leg.