The Norwegian side are second in the standings, level on points with third-place Rapid Vienna, with two rounds of fixtures to go.
Molde's back-to-back defeats against Arsenal has given Rapid a chance to make up a six-point deficit on the Eliteserien champions.
Not since November 2012 have they lost three European games in a row, and they enter this home clash with Dundalk as strong favourites.
The Irish visitors are competing in the competition proper for the second time - an achievement in itself - but have yet to get off the mark with a first point.
The Lilywhites lost 2-1 at home to Molde in the reverse fixture and have since lost to Arsenal and twice to Rapid Vienna.
Excluding qualifying games, Dundalk are now winless in their last 21 away games in all European competitions since winning their first ever such match against FC Zurich in 1963.
The 3-1 home loss to Rapid last time out means that Filippo Giovagnoli's charges can now no longer reach the first knockout stage.
It is all to play for as far as Molde are concerned, though, with a chance to open up a three-point margin on matchday six opponents Rapid, who face Arsenal on Thursday.
The hosts enter this game on the back of two wins in their last three in all competitions. Dundalk have an identical record, including a 11-0 cup win at Athlone Town on Sunday.
Molde have won all three of their previous meetings with Irish opponents, meanwhile, whereas Dundalk lost 2-1 to Rosenborg in their only previous encounter with a Norwegian side.
Molde Europa League form: WWLL
Molde form (all competitions): WLDWLW
Dundalk Europa League form: LLLL
Dundalk form (all competitions): DLLWLW
Patrick McEleney was one of nine different scorers in Dundalk's record win over Athlone, on top of providing five assists, which will do his chances of starting this game no harm.
Giovagnoli made four changes to his lineup for that game and, despite being out of the competition, he is expected to go with his strongest possible XI on Thursday.
Molde have a settled system and not many changes - if any - are expected from last time out.
Molde possible starting lineup:
Linde; Wingo, Gregersen, Sinyan, Risa; Aursnes, Hussain; Hestad, Eikrem, Elingsen; James
Dundalk possible starting lineup:
Rogers; Cleary, Boyle, Hoare; Gannon, Sloggett, Shields, Dummigan; Colovic, McMillan, Duffy
We say: Molde 3-1 Dundalk
Dundalk may have lost all four of their Group B matches - and eight in a row overall in the competition - but they have at least scored in three of those defeats.
This will not be a straightforward game for Molde, but they have won four and drawn one of their last six home games and will surely have enough quality to pick up the points here.