As it stands, Molde hold a three-point advantage over their next opponents in Group F, and there is a scenario where they could establish a six-point lead over third place with victory in Ireland.
Match preview
Having been drawn alongside Gent, Molde and Djurgardens IF, Shamrock Rovers boss Stephen Bradley would have felt like his side had a realistic chance of progressing into the last 32.
As it stands, Rovers remain the only team to take points off Djurgardens, the group leaders, but they have been outclassed in their other two outings.
Trips to Belgium and Norway to face Gent and Molde have ended in 3-0 defeats, Shamrock now one of just two teams yet to score in the group stages.
Their fortunes will need to dramatically change if they are to remain in contention for the top two, something which will not be lost on Bradley as he is forced to deploy attack-minded tactics for this game.
Shamrock have at least remained on top of the League Of Ireland Premier Division, prevailing in their three most recent games to retain a five-point lead.
From Molde's perspective, they are craving a prolonged European run at a time when they already hold a 15-point lead in Norway's top flight.
A dramatic 3-2 defeat to Djurgardens on matchday two was certainly not in the script, but MFK at least responded with a routine win against Shamrock last week.
Ola Brynhildsen scored the opening two goals of that contest, and the newly-capped Norway international now has four strikes from his last three outings.
With the group leaders and a trip to Gent still to come, Erling Moe will recognise that his team, who currently occupy joint-second in this group, need to take advantage of their visit to Dublin.
Shamrock Rovers Europa Conference League form:
D
L
L
Shamrock Rovers form (all competitions):
L
D
W
W
L
W
Molde Europa Conference League form:
L
L
W
D
L
W
Molde form (all competitions):
W
L
W
W
W
W
Team News
Having made six changes to his Shamrock Rovers XI at the weekend, Bradley has options available if he wishes to tinker with his side.
Sean Hoare and Sean Kavanagh could return in defence and at wing-back respectively, while Rory Gaffney could get the nod down the centre of the attack after his goal against Shelbourne.
Ronan Finn should also feature, whether that be in a deeper central-midfield role or in a more advanced position behind the striker.
Barring any injuries, Moe may feel that he has little reason to make any alterations to his in-form Molde side.
However, David Datro Fofana is available after serving a suspension and could get the nod over Magnus Grodem in the final third.
Shamrock Rovers possible starting lineup:
Mannus; Cleary, Hoare, Grace; Lyons, O'Neill, Finn, Kavanagh; Greene, Ferizaj; Gaffney
Molde possible starting lineup:
Karlstrom; Breivik, Risa, Haugan; Linnes, Mannsverk, Hussain, Eriksen, Lovik; Fofana, Brynhildsen
We say: Shamrock Rovers 0-2 Molde
Despite their position at the top of the domestic standings, there can be no getting away from the fact that Shamrock are considerable underdogs ahead of this match. Although we predict a stronger showing than last week, Molde should still prevail in comfortable fashion.