The hosts drew 1-1 away to Nice last week, while the side from the Czech Republic were involved in a 3-3 draw against Partizan.
Match preview
Despite opening the campaign with a DFB-Pokal defeat, Koln will be content with their start to the season after taking nine points from six league games and progressing to the Europa Conference League group stage.
Steffen Baumgart's side beat Fehervar 4-2 on aggregate in the playoff round to book their place in Group D alongside Nice, Slovacko and Partizan.
They began the group phase with a 1-1 draw against Nice last week in a game that was overshadowed by crowd trouble, which forced the kickoff to be delayed by an hour.
After condemning the violence, the Billy Goats returned to action on Sunday where they fell to a narrow 1-0 defeat to Union Berlin, who moved top of the Bundesliga as a result of the victory.
Koln will now turn their attention to Thursday's encounter where they are looking to end a three-game winless home run in all competitions.
Meanwhile, the visitors dropped down to the Europa Conference League after they were knocked out in the third qualifying round of the Europa League by Fenerbahce.
Slovacko made light work of the playoff round with a comfortable 4-0 aggregate victory over AIK, and they were set to claim a third consecutive win in the competition last week.
Jan Kalabiska netted a brace inside 20 minutes at home to Partizan before the visitors were reduced to 10-men following Kristijan Belic's red card.
Despite boasting a two-goal cushion and a one-man advantage, Slovacko required an 83rd-minute equaliser from Libor Kozak to salvage a point after Partizan fought back after half time to take a 3-2 lead.
As a result of the 3-3 scoreline and a 1-1 draw against Mlada Boleslav at the weekend, Slovacko head to Germany following a winless five-game run in all competitions, although their previous three matches have all finished level.
FC Koln Europa Conference League form:
FC Koln form (all competitions):
FC Slovacko Europa Conference League form:
FC Slovacko form (all competitions):
Team News
Ankle problems will prevent Julian Chabot and Mathias Olesen from featuring for Koln, while Sebastian Andersson and Mark Uth also miss out due to injury issues.
Baumgart rotated his squad for Sunday's defeat to Union, but the likes of Kingsley Schindler, Dejan Ljubicic and Ondrej Duda are expected to return to the starting lineup.
After scoring against Nice last week, Steffen Tigges will also come back into the side to lead the line on Thursday.
As for the visitors, they are also expected to make several changes after resting a number of players for Sunday's 1-1 draw with Mlada Boleslav.
Filip Nguyen will return in goal, and he will be shielded by the central defensive partnership of Stanislav Hofmann and Michal Kadlec.
Meanwhile, Libor Kozak will look to add to the goal he scored against Partizan when he features in the frontline alongside Ondrej Mihalik.
FC Koln possible starting lineup:
Schwabe; Schindler, Kilian, Hubers, Hector; Ljubicic, Skhiri; Thielmann, Duda, Kainz; Tigges
FC Slovacko possible starting lineup:
Nguyen; Reinberk, Hofmann, Kadlec, Kalabiska; Petrzela, Danicek, Havlik, Holzer; Kozak, Mihalik
We say: FC Koln 2-1 FC Slovacko
Although Koln have failed to win any of their last three home games, we think they have enough quality in their squad to beat an FC Slovacko side who are winless in their previous five matches.