The two sides sit level on six points in Group H after winning both of their matches against Scandinavian sides Molde and Hacken.
Match preview
Indeed, only Bayern Munich have prevented Leverkusen from winning all 11 of their matches in all competitions so far this season, which was when the Bavarians held Xabi Alonso's side to a 2-2 draw at the Allianz Arena last month.
As such, Die Werkself have to be regarded as one of the strongest teams in European football on current form, and a major contender to win the Europa League after reaching the semi-finals last season. Their improvement since appointing Alonso a little over a year ago has been stark, especially as the Spaniard inherited them sitting in the Bundesliga's relegation zone.
Fast forward 12 months and an impressive 2-1 win away to Wolfsburg on Saturday maintained their status at the top of their domestic table, with 22 points from eight games. There is a serious chasing pack with Stuttgart, Bayern and Borussia Dortmund all within two points of them, but Leverkusen's fans are beginning to dream of lifting their first ever Bundesliga title.
Leverkusen have won the Europa League before - albeit when it was named the UEFA Cup - when defeating Espanyol on penalties in the 1987-88 campaign. However, with only one DFB-Pokal added to their trophy cabinet since, this is a big club starved of success, and they will be targeting wrapping up qualification to the knockout stages as quickly as possible with successive fixtures against Qarabag on the horizon.
However, the Azerbaijani champions should not be underestimated, having claimed two 1-0 victories against Molde and Hacken from their opening fixtures.
Despite competing in the Europa League group stage on seven previous occasions, The Horsemen have never progressed into the knockout stages of Europe's secondary competition, so Gurban Gurbanov will be desperate to make it eighth time lucky for his side.
After all, the 51-year-old has been through it all with Qarabag having managed them since 2008, dominating Azerbaijani football in recent years by lifting the domestic title in nine of the last 10 seasons. They look well-placed to retain their title this season having accrued 20 points from 10 games, although Zira FK are ahead of them at the top of the table due to head-to-head rules.
Qarabag's crowning moment came when reaching the Champions League group stage for the first and only time in the 2017-18, as they went on to draw with Atletico Madrid in both meetings with Diego Simeone's side. However, that achievement would be topped if they can make it into the knockout stages of the Europa League, with any points they can pick up from their upcoming matches against Leverkusen likely to be viewed as a bonus.
Bayer Leverkusen Europa League form:
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Bayer Leverkusen form (all competitions):
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Qarabag FK Europa League form:
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Team News
Leverkusen will remain without Arthur and Ayman Aourir, who are both sidelined with serious tendon and knee injuries respectively.
Alonso is likely to make some changes for this match, with his priority potentially maintaining their place at the top of the Bundesliga table. As such the likes of Florian Wirtz, Nathan Tella and Robert Andrich are all primed for starts after only being named on the bench for Saturday's victory away to Wolfsburg.
Qarabag could be without Montenegro full-back Marko Vesovic due to a knock, but otherwise Gurbanov appears to have a fully fit squad at his disposal for the long trip to Germany.
The 68-capped Azerbaijan former international may look to reward the same group of players that defeated Hacken 1-0 in Sweden with another start, as they showed they are capable of picking up points on the road as well as at their home fortress: the Azersun Arena.
Bayer Leverkusen possible starting lineup:
Kovar; Kossounou, Tah, Hincapie; Stanisic, Andrich, Amiri, Tella; Wirtz, Hlozek; Schick
Qarabag FK possible starting lineup:
Lunyov; Silva, Guseynov, Medina, Cafarguliyev; Romao, Jankovic; Andrade, Benzia, Zoubir; Juninho
We say: Bayer Leverkusen 1-0 Qarabag FK
If Alonso makes changes en masse as he may be tempted to, this could be a tighter match than many expect, with Qarabag always defensively disciplined under Gurbanov's management.
They will be more confident than usual in European competitions, too, having won both of their opening games, but Leverkusen should still possess enough quality to make it three victories from three in Group H.