However, with the Hammers sitting at the bottom of the Premier League table, the Danish outfit will remain optimistic of pulling off arguably the greatest result in their history.
Match preview
Having brought in numerous quality players to strengthen the squad and kept the services of Declan Rice, West Ham have been tipped to break back into the Premier League's top six this season.
Instead, David Moyes's side sit at the bottom of the table with zero points and goals after defeats to Manchester City, Nottingham Forest and Brighton & Hove Albion.
While the club's supporters were understanding about losing to the defending champions, they have been left frustrated with their team's output in the final third in the following two fixtures.
Even though they got a 3-1 victory over Viborg on the board in the opening fixture of this tie, they had to come through some difficult moments before netting a potentially-pivotal strike through Michail Antonio during the closing stages.
There is still every expectation that they will come through on Thursday with minimal fuss, but a test of character will be required if they concede the first goal in Denmark.
However, Viborg have been equally inconsistent in recent weeks, starting the Danish top-flight campaign with three wins and three defeats.
The latest of those setbacks came against unbeaten Randers at the weekend, although Jacob Friis's team are only four points adrift of top spot.
Facing West Ham is a clear step up in class from what they have previously experienced in this competition, but they have not lost a competitive fixture on home territory since February.
That is something which will not be lost on their English foes, and there remains confidence that they can at least take this tie to extra time if they can rise to the occasion of one of their biggest fixtures in their history.
Viborg FF Europa Conference League form:
Viborg FF form (all competitions):
West Ham United Europa Conference League form:
West Ham United form (all competitions):
Team News
Moyes will want to find a balance between naming a strong West Ham XI and giving further minutes to players who need it when making his team selection for Thursday's game.
Reverting to a back three would help Angelo Ogbonna, who made his long-awaited return from a serious knee injury last week, and Ben Johnson is also expected to return to the team.
Goalkeeper Alphonse Areola will return between the sticks, while Flynn Downes and Gianluca Scamacca should feature, but Rice serves the second and final game of his European ban.
With Brexit rules having prevented his participation last week, Ibrahim Said could return on the flank for Viborg.
Anton Gaaei will again deputise at right-back if Daniel Anyembe does not recover from the injury which led to his first-half withdrawal in the first leg.
Viborg FF possible starting lineup:
Lund; Gaaei, Zaletel, Burgy, Sorensen; Bonde, Gronning, Leemans; Said, Grot, Lonwijk
West Ham United possible starting lineup:
Areola; Johnson, Ogbonna, Kehrer; Coufal, Downes, Soucek, Cornet; Bowen, Scamacca, Lanzini
We say: Viborg FF 1-2 West Ham United (West Ham to win 5-2 on aggregate)
With West Ham possessing very little momentum from the Premier League, we expect Viborg to throw everything at their higher-profile opponents during the early stages. Nevertheless, regardless of Viborg's mentality, West Ham have the greater quality, and that should shine through at some stage.