This tie will see Bosnia & Herzegovina's champions face last season's winners of the Slovakian Super Liga.
Match preview
Indeed, Zrinjski Mostar retained the Premier League of Bosnia and Herzegovina in some style last season, finishing 20 points clear of their nearest competitors Borac Banja Luka in the end.
They went on to progress from a Champions League qualifying tie for the first time in the club's history by overcoming Armenian side Urartu on penalties last week, with Hrvoje Barisic dispatching the winning penalty in sudden death.
Having won 1-0 in Armenia in the first leg, Krunoslav Rendulic's side appeared to be coasting into the second round when Nemanja Bilbija doubled his side's advantage in the tie after 27 minutes, but a late brace from Narek Grigoryan sent the match into extra-time.
Tomislav Kis's penalty put the Bosnians back in control of the tie, but Urartu would not lie down easily, with Artem Maksimenko putting his side back in front on the night before the visitors suffered major heartbreak in the end.
Rendulic will know that his side can ill-afford another home defeat when they host Slovan Bratislava on Tuesday, otherwise they will face an uphill task to advance once again.
Indeed, Slovan Bratislava will head into the tie as favourites to progress after defeating Zrinjski Mostar on penalties at the play-off stage of Europa Conference League qualifying last season, as well as comfortably beating them in this competition 14 years ago.
Having lifted the Slovak Super Liga title for the fifth successive season last time out, Slovakia's most successful club are aiming to reach the group stage of the Champions League for the first time in their history.
The closest they have managed was when reaching the final play-off stage of qualifying in the 2014-15 campaign, when they were defeated by BATE Borisov. However, having regularly competed in the Europa League and Europa Conference League in recent seasons - reaching the last-16 of the latter earlier this year - they clearly possess more European pedigree than their forthcoming opponents.
After surprisingly being held 1-1 at home by Luxembourg side Swift Hesperange in the first round of qualifying, Vladimir Weiss's side ultimately prevailed 3-1 on aggregate, with the head coach's son - who began his career at Manchester City - scoring all three of their goals across the course of the tie.
Weiss Snr will be hoping for another positive result on the road when they arrive in Mostar in midweek, as this would put them in an incredibly strong position to progress from the reverse leg in Bratislava next week.
Zrinjski Mostar Champions League form:
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Slovan Bratislava Champions League form:
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Slovan Bratislava form (all competitions):
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Team News
Zrinjski Mostar are expected to be without Ivan Jukic and Marin Magdic due to injury on Tuesday, with Rendulic unlikely to make any changes to the team that progressed against Urartu last week.
That would mean their star man Mario Cuze taking up his usual spot on the left wing, having made his loan move from Dinamo Zagreb permanent earlier this summer after scoring eight goals in 32 league games last season.
Slovan Bratislava, meanwhile, will travel without Martin Trnovsky, Cesar Blackman and Adler due to injury.
Captain Weiss will likely start from the left flank, but former Watford midfielder Juraj Kucka may not reclaim his place in midfield after being sent off against Swift Hesperange.
Zrinjski Mostar possible starting lineup:
Maric; Corluka, Senic, Barisic, Marin; Stanic, Canadjija, Ivancic; Ticinovic, Bilbja, Cuze
Slovan Bratislava possible starting lineup:
Borjan; Bajric, Kashia, Wimmer, Lovat; Kankava, Savvidis; Barseghyan, Tolic, Weiss; Cavric
We say: Zrinjski Mostar 1-2 Slovan Bratislava
These sides will remember each other well after meeting at the final hurdle of qualifying for the Europa Conference League last season, with Slovan Bratislava ultimately prevailing from that tie on penalties.
There is little doubt that the Slovakian champions possess both greater European pedigree and individual quality, and we can envisage them gaining an impressive victory in Mostar on Tuesday.