The Slovenian hosts were dumped out of the Champions League preliminary rounds by Ludogorets Razgrad, while Zalgiris were sent packing by Ferencvaros 5-1 on aggregate.
Navigating a two-legged tie with Shkendija without conceding a goal - and storming to a 6-0 aggregate success - seemed to set Mura up for the ideal start to their campaign, but it has not panned out that way for the Slovenian champions.
Ante Simundza's side were able to hold Ludogorets to a goalless draw in the first leg of their Champions League second qualifying round tie, but the quality of the Bulgarians soon shone through in the second leg as Pieros Sotiriou, Cauly and Elvis Manu all netted in a routine 3-1 win.
Furthermore, Simundza has overseen a woeful start to his side's title defence in the Slovenian top flight - taking just one point from a possible nine so far - and the Black and Whites are now winless in five games across all competitions ahead of Thursday's first leg.
Mura did manage to progress as far as the Europa League playoff round in the 2012-13 campaign, although they were quickly seen off by Lazio that year, and another shot at that elusive first group-stage appearance could go begging unless Simundza can inspire a sudden turnaround in fortunes.
Similarly, Zalgiris' short-lived Champions League campaign saw the Lithuanian outfit cruise to victory during the first round of qualifying, as they were simply too strong for Northern Irish side Linfield in a 5-2 aggregate success.
However, the second-round curse would bedevil Zalgiris for the sixth time in a row, as Ferencvaros claimed a 2-0 win on home turf before travelling to Lithuania to finish the job with a 3-1 second-leg success, forcing their opponents to drop down to the Europa League once more.
Zalgiris have now bowed out in the second round of qualification during all six of their Champions League campaigns since 1993, while they have also never managed to advance past this stage of the Europa League, suffering third-round qualifying defeats to Lech Poznan and Sevilla in 2013-14 and 2018-19 respectively.
Vladimir Cheburin's side continue to assert their dominance domestically, however, as Zalgiris - the reigning A Lyga champions - sit at the top of the standings after 19 games and have strung together an eight-game unbeaten run domestically, winning six of them.
The winners of this tie will meet Austrian side Sturm Graz for the right to advance to the Europa League group stages, and the importance of a positive first-leg result cannot be understated for both of these hopefuls.
Mura ought to persist with their three-at-the-back system in spite of recent results, with Jan Gorenc potentially returning to the rearguard after watching on from the bench against NK Bravo at the weekend.
Tomi Horvat - who scored his side's only goal over two legs against Ludogorets - should also earn a recall to the midfield, which could in turn see Stanisa Mandic drop out of the attack as Amadej Marosa moves further forward.
The Lithuanian champions have not had any domestic duties to fulfil since suffering defeat to Ferencvaros and could therefore largely stick with the same XI here, although Josip Tadic will hope to come in to the attack ahead of Jakub Sylvestr.
NS Mura possible starting lineup:
Obradovic; Karnicnik, Gorenc, Marusko; Kous, Horvat, Kozar, Sturm; Bobicanec; Marosa, K. Cipot
FK Zalgiris possible starting lineup:
Gertmonas; Mikoliunas, Diaw, Ljubisavljevic, Bopesu; Onazi, Verbickas, Kuklys; Kyeremeh, Tadic, Videmont
We say: NS Mura 0-1 FK Zalgiris
The first leg should be a closer affair than the form book would suggest, with Mura aiming to push their domestic troubles to one side while Zalgiris seek to keep the momentum going from their dominant league form.
With Simundza's men shutting out the opposition in three of their four Champions League games and Zalgiris developing a fondness for away clean sheets, it is difficult to envisage many goals in this encounter, but we still expect the visitors to just edge the first leg.
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