Cukaricki ousted Racing FC of Luxembourg to reach this stage, while FC Twente qualified for this round directly after finishing fourth in the Eredivisie last season.
Match preview
Serbian side Cukaricki, who are based in Belgrade, thrashed Racing 8-1 on aggregate to reach the third qualifying round of this competition for the second successive season.
Head coach Dusan Kerkez, who is in his first season in charge of the club, will be hoping to go at least one better than his predecessor, with The Highlanders also hoping to qualify beyond the qualifying stages of European competition for the first time in their history.
They are clearly a side on the up, though, having recorded back-to-back third-placed finishes in the Serbian SuperLiga.
However, there is little doubt they head into Thursday's clash as massive underdogs, undoubtedly requiring a positive result to protect on their travels to the Netherlands next week.
Indeed, FC Twente are on the road to recovery themselves after a dismal period which culminated in them being relegated to the Eerste Division at the end of the 2017-18 season.
This came less than a decade after their historic Eredivisie triumph under former England manager Steve McClaren in 2009-10, with the Dutch side reaching the quarter-finals of the Europa League in the following campaign.
However, they were banned from European competition for three years in 2015 due to irregular transfer activities, starting a downward spiral which has proven tough for them to come back from.
The Tukkers now have the chance to reach the group stages of European competition for the first time in 10 years, though, with them heading into the two-legged affair against Cukaricki as huge favourites to progress.
Cukaricki Europa Conference League form:
Cukaricki form (all competitions):
Team News
Cukaricki do not appear to have any injury issues heading into Thursday's encounter.
As such, Kerkez is likely to pick the same XI which comfortably dispatched Racing 4-0 last week.
FC Twente, meanwhile, will travel without defender Robin Propper due to an ankle injury.
Ron Jans's side wrapped up their pre-season preparations with an impressive 4-1 win against Serie A outfit Bologna at the weekend.
It would be a surprise if any changes were made from that starting line-up, with former Norwich City striker Ricky van Wolfswinkel set to lead the line.
Cukaricki possible starting lineup:
Belic; Rogan, Vujadinovic, Drezgic, Roganovic; Mijailovic, Docic, Kovac; N'Diaye, Badamosi, Ivanovic
FC Twente possible starting lineup:
Unnerstall; Brenat, Hilgers, Pleguezuelo, Smal; Zerrouki, Sadilek; Misidjan, Vlap, Rots; Van Wolfswinkel
We say: Cukaricki 1-2 FC Twente
Cukaricki will hope to catch FC Twente cold given that it is the Dutch side's first competitive match of the season.
While we would not be surprised to see the Serbian side keep things competitive, we expect the visitors to have a little too much quality and secure a narrow victory as a result.