Lille won 2-0 on the opening matchday in Group A, while KI were defeated 2-1 by Slovan Bratislava.
Match preview
Competing in their first ever group match in a European competition, KI actually took the lead in the Slovakian capital through Deni Pavlovic's 48th-minute strike, but Vladimir Weiss and Aleksandar Cavric struck back to send their opponents home empty-handed.
The 20-time Faroe Islands Premier League champions performed remarkably well during qualifying, knocking out Ferencvaros and BK Hacken out of the Champions League before narrowly falling short against Molde and Sheriff Tiraspol to ultimately drop down to Europe's third competition.
However, excluding the now defunct Intertoto Cup, KI are the first Faroese team to reach the group stage of any European competition in history, making their achievement very impressive regardless of how their progress unfolds between now and mid-December.
Given how closely they pushed Slovan Bratislava away from home on matchday one, Magne Hoseth will retain full belief that they can challenge their French opponents, especially with home support on their side on Thursday.
However, Lille will bring plenty of European pedigree with them to Klaksvik, having competed in the Champions League group stage on seven occasions since the turn of the century.
The 2020-21 Ligue 1 champions reached the last-16 of Europe's elite competition in the following season, losing out to Chelsea on that occasion, which matched their best effort in either of Europe's main tournaments.
Since stunning Paris Saint-Germain to lift their domestic title for the fourth time in the club's history, Lille have dropped off domestically, with 10th-placed and fifth-placed finishes seeing them miss out on Europe's elite competition. They moved up to seventh in Ligue 1 by winning away to Le Havre on Sunday.
On the flipside, though, Paulo Fonseca and his players will be viewing the Europa Conference League as a competition which they can win. Following their 2-0 win against Olimpija last time out in this tournament, they will be in excellent shape to cruise into the knockout stages if they can gather all three points in the Faroe Islands this week.
KI Klaksvik Europa Conference League form:
L
KI Klaksvik form (all competitions):
W
W
L
D
L
L
Lille Europa Conference League form:
W
D
W
Lille form (all competitions):
D
W
D
W
L
W
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Team News
Having performed above expectations to almost gain a positive result in Bratislava two weeks ago, Hoseth could reward the same group of players with another start on Thursday.
As such, Hallur Hansson may be disappointed to miss out having been left on the bench during that defeat, with Pavlovic set to retain his place within the hosts' engine room.
Lille, meanwhile, will travel without Yusuf Yazici, Samuel Umtiti, Nabil Bentaleb and Adam Ounas due to injury.
Unless Fonseca decides to rest several key players, Canada forward Jonathan David will almost certainly lead the line for the visitors, having scored from the penalty spot against Olimpija.
KI Klaksvik possible starting lineup:
Johansson; Petersen, Faero, Forren; Danielsen, Pavlovic, Andreasen, Da Silva; Frederiksberg, Gussias, Mikkelsen
Lille possible starting lineup:
Chevalier; Santos, Diakite, Alexsandro, Gudmundsson; Andre, Gomes; Zhegrova, Haraldsson, Cavaleiro; David
We say: KI Klaksvik 0-2 Lille
Although KI acquitted themselves extremely well on the European stage once again when falling to defeat against Slovan Bratislava last time out, they will be facing a step-up in class when hosting Lille this week.
The visitors are generally defensively secure and are unlikely to give their opponents many chances in transition, which should help them cruise to a comfortable victory in the end.