The Hammers secured a 2-0 advantage during the away first leg in Cyprus, setting them up to get the job done at the London Stadium.
Match preview
With West Ham having won just two of their last 14 matches in the Premier League, David Moyes will appreciate having European football as an avenue to keep him in a job.
Although ensuring that the Hammers remain in the top flight is far more important, the Scot knows that lifting the club's first-ever trophy on the continent is a realistic possibility.
As it stands, West Ham are making full use of being handed one of the more favourable draws in the last 16 having prevailed 2-0 on away territory last week.
Two goals in the nine minutes before half time from Michail Antonio put West Ham well on their way to the win, and they successfully saw out the second half without conceding a tie-changing strike.
While the job is not complete, Moyes and his players know that they are in a commanding position ahead of trying to emerge victorious for the 10th successive time in this competition.
West Ham head into this fixture having been held to a 1-1 draw by Aston Villa on Sunday, with the discontent among the fanbase something which will only encourage AEK Larnaca.
The Guardians have already broken new ground this campaign, a third-placed finish in their Europa League group leading to a narrow success over Dnipro-1 in the playoff round of this competition.
All things considered, this tie is a step too far for Jose Luis Oltra's team, particularly at a time when they have lost three of their last four league matches.
They currently face a three-point gap to top spot, something which they may be happy to prioritise having enjoyed a prolonged run in Europe.
West Ham United Europa Conference League form:
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W
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W
West Ham United form (all competitions):
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AEK Larnaca Europa Conference League form:
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D
L
AEK Larnaca form (all competitions):
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D
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W
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L
Team News
West Ham will be without Flynn Downes after the midfielder collected his third yellow card of the competition in the first leg.
Tomas Soucek should start in his place, while rotation is expected in numerous positions with Ben Johnson, Angelo Ogbonna, Aaron Cresswell, Pablo Fornals and Manuel Lanzini all expected to feature.
Gianluca Scamacca could be recalled, despite recent criticism from Moyes, but Maxwel Cornet may not be risked from the first XI at this stage after a long-term absence.
Left-back Angel Garcia and midfielder Pere Pons are both available for Larnaca after serving one-match bans for the first leg.
Having been introduced as straight replacements, Nikolas Englezou and Rafail Mamas could drop down to the substitutes' bench.
West Ham United possible starting lineup:
Areola; Johnson, Ogbonna, Aguerd, Cresswell; Rice, Soucek; Fornals, Lanzini, Benrahma; Scamacca
AEK Larnaca possible starting lineup:
Piric; Casas, Milicevic, Tomovic, Garcia; Ledes, Pons; Rosales, Sanjurjo, Jakolis; Lopes
We say: West Ham United 2-0 AEK Larnaca
With no Premier League or FA Cup fixture at the weekend, West Ham can place full focus on this contest. Even if the odd alteration is made, the Hammers have the tools to make this match as routine as they want, and it could prove to be a long night for the visitors.