Just one point separates the top three sides in Group C after two matches, but Liverpool will be hoping for maximum points from back-to-back games against Red Star, who were thrashed by Paris Saint-Germain last time out.
Liverpool's season so far has been defined by either grinding out ugly wins or failing to win by as many as they should given the chances they create.
In many ways, Reds fans will be happy with that. For too long Liverpool have dropped points in matches just like Saturday's trip to Huddersfield Town, when they were far from their best but still managed to scrape a win.
Mohamed Salah's goal at the John Smith's Stadium saw Jurgen Klopp's side return to winning ways after a four-match run without a victory, keeping them level on points with Manchester City at the top of the Premier League table in the process.
It is certainly a position supporters would have taken after nine games had it been offered to them at the beginning of the season, and while it is unlikely that they will be able to sustain such form unless they do eventually reach the levels they are capable of, the fact that they have made their best-ever start to a Premier League campaign and still have vast room for improvement will be encouraging.
It was in the Champions League last season that Liverpool showcased those levels they will be aspiring to again this term - particularly going forward, when Salah, Sadio Mane and Roberto Firmino established themselves as the most prolific attacking trio in the competition's history en route to the final.
There was more evidence of that on matchday one when they beat a Paris Saint-Germain side that have swept all others in front of them this season, although the attacking flair abandoned them on their last Champions League trip.
Many of Liverpool's defining European displays of 2017-18 came away from home, but they could have no complaints at leaving the Stadio San Paolo empty-handed earlier this month - even if Napoli needed a last-gasp winner to take all three points.
The Reds have now lost three of their last four Champions League games, although at Anfield they are unbeaten in their last 17 European outings in a run which stretches back to October 2014.
Klopp's side could be forced to lean on that home form in order to get through what is a difficult group, and anything other than a win against the team which looks weakest on paper could prove to be a costly slip-up on a night where at least one of PSG or Napoli are guaranteed to drop points.
Recent Champions League form: WL
Recent form (all competitions): WLDLDW
For a team which has become accustomed to winning, Red Star's 6-1 defeat at the hands of PSG on matchday two would have come as a sharp wake-up call.
The Serbian outfit may not have been expecting to challenge for a place in the last 16 having been drawn alongside PSG, Liverpool and Napoli, but their goalless draw with the latter on matchday one will have given them hope that they could at least hold their own.
A response will be expected to their joint-heaviest ever European defeat, although Anfield is perhaps not the most likely place for it to happen.
The opening two games in this group stage suggest that Red Star will instead need to rely on their home form to take points off their more illustrious opponents, although they have only lost two of their last nine European away games.
Many of those have come against teams of a different calibre entirely to those Red Star find themselves up against now, though, with the 2018-19 campaign being their first in the Champions League proper having finally made it through the qualifying stages at the seventh attempt.
Vladan Milojevic's side have overcome teams from Latvia, Lithuania, Slovakia and Austria to make it this far, so then being thrown into games against three of Europe's heavyweights is a tough ask.
Liverpool must not fall into the trap of regarding Red Star as whipping boys, though; the Serbian champions have lost just three of their last 19 European outings and the defeat to PSG - as heavy as it was - is their only defeat in their last 38 matches across all competitions.
Domestically, Serbia's most successful club are currently on a 38-game unbeaten run in the league - including 34 wins - to help build a seven-point lead at the top after only 12 matches of the new campaign.
Red Star will not be the last club to be on the wrong end of a big score against PSG this season, but the challenge for them now is to learn from that drubbing and avoid a similar fate against another talented attack.
Recent Champions League form: DL
Recent form (all competitions): WWLWWW
Liverpool captain Jordan Henderson was taken off at half time of his side's match against Huddersfield at the weekend after complaining of a tight hamstring, so he is unlikely to be risked for this match.
Firmino was also named on the bench at Huddersfield and is expected to return, while Mane remains a doubt due to the thumb injury he sustained on international duty.
Trent Alexander-Arnold could be handed a recall at right-back having missed the past two games, leaving Klopp with a decision whether to start Joe Gomez or Dejan Lovren alongside Virgil van Dijk in defence.
Red Star are also expected to be without their captain after Vujadin Savic was taken off at half time against PSG and has not featured since.
Filip Stojkovic is also a doubt for the visitors after he was replaced just 36 minutes in to his side's Belgrade derby against Rad on Saturday.
Richmond Boakye scored twice in that game to take his tally to five goals in four league games this season, and he is likely to be one of Red Star's main attacking threats at Anfield.
Liverpool possible starting lineup:
Alisson; Alexander-Arnold, Lovren, Van Dijk, Robertson; Milner, Fabinho, Wijnaldum; Salah, Firmino, Shaqiri
Red Star possible starting lineup:
Borjan; Sumaila, Degenek, Babic, Rodic; Ebecilio, Jovicic, Ben, Krsticic, Marin; Boakye
Head To Head
These two sides have only met twice before, the first of which came exactly 45 years to the day before this match. Red Star ran out 2-1 winners in both legs of their 1973-74 European Cup tie to reach the quarter-finals.
Indeed, Red Star were the team to inflict Liverpool's first ever European defeat at Anfield, and the second did not arrive for another 18 years.
Liverpool have no other experience of facing Serbian teams, but Red Star have lost just one of their last six visits to England, including a goalless draw with Arsenal at the Emirates Stadium in last season's Europa League group stages.
We say: Liverpool 3-0 Red Star
Liverpool have not been firing on all cylinders so far this season, but a European night under the lights always gets the fans and the team fired up. A similar display to their matchday one victory over PSG should see the hosts run out fairly comfortable winners.