The second-round qualifying tie is finely poised after the two sides played out a 1-1 draw in Slovenia last Wednesday.
Match preview
Slovan Bratislava are competing in Champions League qualifying for the sixth consecutive season after they retained their Fortuna Liga title last term.
The Slovakian side began their European campaign with a 6-3 aggregate victory over North Macedonian side Struga to set up a clash with Celje.
They would have been content with their performance in the first leg, with David Strelec striking in the 11th minute to cancel out Luka Bobicanec's early effort, before Slovan Bratislava saw out the majority of the contest with 10 men following Kyriakos Savvidis's red card.
Slovana Bratislava turned their attention to league action on Saturday as they cruised to a 4-1 victory against Komarno on matchday one of the Fortuna Liga season.
The Slovakian champions will now be fully focused on Tuesday's European clash, with the home side looking to reach the third round of Champions League qualifying for the second season in a row.
Celje are participating in Champions League qualifying for the first time since the 2020-21 season after they won the Slovenian PrvaLiga last season.
The Slovenian champions breezed through the first qualifying round with a comprehensive 7-1 aggregate win over Flora.
After winning both of their legs against Flora, Celja went on to beat Bravo 2-1 in their opening league game to record a third consecutive victory.
However, their winning run came to an end with a 1-1 draw in last week's first leg, leaving them with work to do in the away leg if they are to reach the third round of Champions League qualifying for the first time.
Celje, who was not in action at the weekend, may be able to take confidence from the fact that they have won three of their last four European away games.
Slovan Bratislava Champions League form:
W
W
D
Slovan Bratislava form (all competitions):
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W
D
W
Celje Champions League form:
W
W
D
Celje form (all competitions):
Team News
Slovan Bratislava boss Vladimir Weiss could select Julius Szoke to replace the suspended Savvidis.
At the back, Weis is likely to stick with the trio of Kenan Bajric, Guram Kashia and Kevin Wimmer following a relatively strong defensive display in the first leg.
Having scored in the last two matches, Strelec will be looking to continue his fine form when he leads the line on Tuesday.
As for the visitors, they will have to assess Tamar Svetlin's fitness after the midfielder was forced off in the first half of the first leg.
If Svetlin is unable to feature, Celje boss Damir Krznar could present Mario Kvesic with a starting opportunity.
Lithuania international Armandas Kucys is set to lead the line, with forward likely to be joined in the front three by Aljosa Matko and Luka Menalo.
Slovan Bratislava possible starting lineup:
Takac; Bajric, Kashia, Wimmer; Blackman, Szoke, Kucka, Zuberu; Mak, Weiss, Strelec
Celje possible starting lineup:
Stubljar; Karnicnik, Vuklisevic, Zec, Krefl; Kvesic, Pisek, Bobicanec; Matko, Menalo, Kucys
We say: Slovan Bratislava 2-1 Celje
Slovan Bratislava would have been pleased with the first-leg draw, especially as they played the majority of the game with a numerical advantage.
We think the Slovakian champions will now make full use of home advantage to claim a narrow win and advance into the next round.