The Reds have drawn both of their Group E matches so far, but face a team who have picked up just one point from their own two outings.
Maribor went into the group stages as the biggest outsiders to make it through to the last 16 of the Champions League, but they will be hopeful of taking advantage of an out-of-form Liverpool side on Tuesday.
The Slovenians needed an 85th-minute winner to rescue a point at home to Spartak Moscow on the opening matchday, but they were comfortably beaten last time out when Sevilla ran out 3-0 victors.
Should they earn anything from the upcoming double-header against Liverpool then it would be something of a surprise considering that they have only ever won one of their 14 games in the Champions League group stages, with that victory coming in their first ever appearance in the competition proper back in September 1999.
Maribor have drawn five and lost eight of their 13 group games in this competition since then, failing to score more than once in any of those matches and suffering exit from the competition in the groups on the two previous occasions they have reached the Champions League proper.
The most recent of those before this season came in 2014-15, although the Slovenian champions can take some inspiration from that campaign heading into Tuesday's match having earned a 1-1 draw at home to Chelsea in their most recent meeting with an English club.
However, they have never won a home Champions League group game in seven previous attempts, drawing three and losing four to pick up only three points from a possible 21 in front of their own fans.
Across all competitions, the defeat to Sevilla is Maribor's only loss in their last 11 outings stretching back to August, although they have a fight on their hands to retain the Slovenian title despite being unbeaten domestically so far this campaign.
Darko Milanic's side currently trail Olimpija by two points at the top of the Slovenian league, and as things stand they would have to settle for Europa League football next season.
Of course, there is still a long way to go both on the domestic and European fronts, and Maribor may be optimistic about their chances of improving their position in the latter on Tuesday having not been beaten at home in any competition this season.
The Slovenian outfit have drawn their last three games in front of their own fans, but that would be regarded as a decent result against the five-time champions of Europe.
Recent Champions League form: DL
Recent form (all competitions): DWWLDW
It has been a tale of frustration and missed opportunities in the Champions League for Liverpool so far this season, with draws against Sevilla and Spartak Moscow leaving them on two points from as many games in Group E.
The Reds had the chances to win both games, but instead their wait for a win in this competition now stretches back to September 2014 - a seven-game streak which constitutes Liverpool's worst ever Champions League run.
The last four of those matches have all ended as draws, while you have to go back to a 1-0 win over Debrecen in November 2009 for both Liverpool's most recent away Champions League win and their last clean sheet in the competition.
Jurgen Klopp's side have not exactly been in winning form elsewhere of late either, picking up just one victory from their last eight matches across all competitions with a mixture of defensive frailties and wastefulness in the final third hurting Liverpool in that time.
Saturday's lunchtime kickoff against bitter rivals Manchester United brought with it more frustration as Liverpool failed to break down a defensive and resolute Jose Mourinho side, being forced to settle for a goalless draw at Anfield.
It is now three draws in a row across all competitions and, with fellow top-four hopefuls Tottenham Hotspur next up in the Premier League on Sunday, Liverpool will know that a return to form against Maribor would come in timely fashion.
The Reds have only won twice on the road all season, though, and in the Champions League proper they have won just one of their last eight away trips, stretching back to a 1-0 triumph over Real Madrid in February 2009.
That 2008-09 campaign was the last time Liverpool reached the knockout stages of this competition, and that wait may continue if Klopp's side don't improve at both ends of the field over the double-header with Maribor.
Liverpool have had 29 more shots than their opponents over their first two group games, yet still find themselves looking for their first win having conceded three goals from the four shots on target they have faced so far.
Recent Champions League form: DD
Recent form (all competitions): DLWDDD
Klopp has confirmed that Loris Karius will start in goal once again for Liverpool, as he has done in both Champions League group games so far this season.
However, the Liverpool boss played down the possibility of making sweeping changes to his side, who are heading into their second of three games in an eight-day period.
Maribor possible starting lineup:
Handanovic; Milec, Rajcevic, Billong, Viler; Pihler, Kabha, Vrhovec, Bohar; Ahmedi; Tavares
Liverpool possible starting lineup:
Karius; Alexander-Arnold, Lovren, Matip, Robertson; Wijnaldum, Henderson, Oxlade-Chamberlain; Salah, Firmino, Coutinho
Head To Head
This will be the first ever meeting between these two sides, and only Liverpool's second ever tie against Slovenian opposition.
The Reds also took on Olimpija Ljubljana in the first round of the 2003-04 UEFA Cup, being held to a 1-1 draw in Slovenia but winning the reverse 3-0 at Anfield.
Maribor, meanwhile, have won just one of their eight previous encounters with English clubs, beating Wigan Athletic 2-1 in the 2013-14 Europa League group stages.
We say: Maribor 0-2 Liverpool
Liverpool may not be in particularly good form, but they will still be expected to win against Maribor on Tuesday. The Reds have dominated both of their Champions League fixtures so far and only need to find their killer instinct in front of goal to get back onto the winning trail.