Meanwhile, their Hungarian opponents make the trip to Germany having already prevailed through two rounds in this competition.
Match preview
For a club of FC Koln's size, one European campaign in 25 years is far from acceptable, and that will not be lost on Steffen Baumgart.
He has already worked wonders to transform the club from relegation contenders to a top-half team in the space of a year, and there is genuine expectation that they can go deep in this continental competition.
After the embarrassment of being eliminated from the DFB-Pokal by Jahn Regensburg, this is a squad which have now refocused and enter this tie on collecting four points from a Bundesliga double-header with Schalke 04 and RB Leipzig.
The Billy Goats twice came from behind to earn a point at the home of the latter, an important result which keeps him in the running for top spot when neither Bayern Munich or Borussia Dortmund are on their schedule until September 30.
On a negative note, Anthony Modeste has left for Dortmund, and Baumgart will hope that Florian Dietz can make the seamless transition to the senior squad after a productive spell with the club's reserve side.
From Fehervar's perspective, they make the trip to Germany having suffered a 4-0 defeat at the hands of Ferencvaros at the weekend.
That may be a sign that this tie could prove one too far for the Hungarian side, who have beat Qabala and Petrocub to reach this stage of the competition.
Back in 2018-19, they earned a draw at home to eventual Europa League winners Chelsea during the group stages, but that remains the last occasion when they featured in the main stages of a European competition.
Michael Boris's side currently sit in seventh position in the Hungarian top flight having lost two of their three opening fixtures.
FC Koln form (all competitions):
Fehervar Europa Conference League form:
Fehervar form (all competitions):
Team News
Only four members of FC Koln's squad have played the full 180 minutes in the Bundesliga this campaign, an indication that Baumgart may be comfortable in making changes on Thursday.
Nevertheless, each of his five substitutions against RB Leipzig on Saturday came by the 73rd-minute mark, so his first XI from that fixture should be well-rested.
Benno Schmitz could be restored at right-back but that could prove to be the only change to the team.
Kenan Kodro may miss out for the visitors after having to be withdrawn during the first half against Ferencvaros.
Budu Zivzivadze could take his place in attack, but with some players being well-rested after their half-time substitutions at the weekend, Boris may opt to retain the rest of his starting lineup.
FC Koln possible starting lineup:
Schwabe; Schmitz, Hubers, Kilian, Hector; Skhiri, Martel; Thielmann, Ljubicic, Kainz; Dietz
Fehervar possible starting lineup:
Kovacs; Fiota, Shabanov, Stopira; Nego, Bumba, Pinto, Heister; Dardai, Petryak; Zivzivadze
We say: FC Koln 3-0 Fehervar
Having already been eliminated in Germany's premier cup competition, FC Koln will be taking this tournament even more seriously. With that in mind, we expect a strong showing from the home side, one which may lead to the tie effectively being over before the reverse fixture in Hungary.