The winners of this tie on aggregate will progress to the playoff round to face either Malmo or PAOK later this month.
Match preview
Shamrock Rovers are facing an uphill battle to qualify for the main stage of the Europa League for just the second time in their history, after they suffered a 1-0 first-leg defeat to Celje on home soil last week.
Luka Menalo fired home the only goal of the closely-fought contest midway through the first half, ensuring that Celje take a narrow advantage to Dublin.
Hoops head coach Stephen Bradley vented his frustration at the Slovenian side's "disgraceful" pitch after the match, claiming his "whole game plan changed" as a result, but he was pleased with the way his side performed and "created a lot of opportunities" given the circumstances.
Shamrock Rovers have since played out a 1-1 draw with Drogheda United in the League of Ireland Premier on Sunday, with Darragh Burns's sixth-minute opener cancelled out by a second-half strike from Douglas James-Taylor to dent their slim title hopes.
Bradley's men - who sit fifth in the Irish top-flight standings and 10 points behind leaders Shelbourne, who have played a game more - must now shift their attention back to the Europa League and will attempt to improve their home form having won just four of their last 10 games at Tallaght Stadium in all competitions.
Celje suffered a heavy 6-1 aggregate defeat to Slovan Bratislava in the Champions League second round qualifiers to drop down into the Europa League qualifiers, but they bounced back to grind out a hard-fought first-leg win over Shamrock Rovers last week.
The reigning Slovenian PrvaLiga champions have since beaten Radomlje by a 4-2 scoreline in their third match of the new league season on Sunday, with two late goals from Damjan Vuklisevic and Armandas Kucys enough to edge past the visitors, who had initially come from two goals down to restore parity.
Albert Riera, who was re-appointed Celje head coach in July, has suggested that his predecessor Damir Krznar has left him with a squad of players who have 'problem with physical fitness' and that must be resolved quickly with "intensive training".
Celje's busy fixture schedule is not helping their cause, with at least four more matches to prepare for this month, starting with Thursday's second-leg clash against Shamrock Rovers followed by three league games and a potential Europa League playoff.
Taking a one-goal lead to Ireland, the Yellow and Blues are seeking to finish the job as they endeavour to move one step closer to qualifying for the main stage of a European competition for the first time in their 104-year history.
Shamrock Rovers Europa League form:
L
Shamrock Rovers form (all competitions):
W
L
L
W
L
D
Celje Europa League form:
W
Celje form (all competitions):
W
D
L
L
W
W
Team News
Shamrock Rovers are still having to cope without attacking duo Johnny Kenny and Rory Gaffney due to injury; the former is their top scorer with 10 goals this season and requires a few more weeks in the treatment room.
Aaron Greene led the line in the first leg and is expected to retain his spot up front, with Darragh Nugent and Neil Farrugia potentially providing support in the final third.
Sean Hoare, Dylan Watts and Trevor Clarke could also be recalled to the first XI, meaning Sean Kavanagh, Jack Byrne and Cory O'Sullivan are at risk of dropping to the substitutes' bench.
As for Celje, they will assess the fitness of midfielder Tamar Svetlin who has missed the last four matches with an unspecified issue.
Defender Damjan Vuklisevic was suspended for the first leg, but he is available to return on Thursday and could start at the heart of a three-man backline at the expense of Marco Dulca.
Armandas Kucys played the full 90 minutes against Radomlje last time out, but he is expected to continue up front against Shamrock Rovers, with Jost Pisek and Aljosa Matko the most likely duo to provide support in attack.
Shamrock Rovers possible starting lineup:
Pohls; Cleary, Lopes, Hoare; Honohan, Watts, O'Neill, Clarke; Nugent, Farrugia; Greene
Celje possible starting lineup:
Stubljar; Zec, Vuklisevic, Nemanic; Menalo, Bobicanec, Kvesic, Vuklisevic; Matko, Kucys, Pisek
We say: Shamrock Rovers 2-1 Celje (2-2 on aggregate a.e.t - Shamrock Rovers to win on penalties)
There was little to separate the two teams in the first leg and another tight affair could be in store on Thursday. Against a jaded Celje outfit struggling with fitness issues addressed by their own manager, Shamrock Rovers could be spurred on by the home crowd to victory in a contest that may go beyond the 90 minutes.