Defeat to Napoli last time out has put the Reds in an awkward position with Paris Saint-Germain also in the pool, meaning goal difference could be the key at the conclusion of Group C.
Red Star picked up a point in their opener against the Partenopei but were outclassed 6-1 by PSG and look set to prop up the pool.
Liverpool struggled to find their form in Saturday's 1-0 win at Huddersfield and Jurgen Klopp has questions over who will make his starting XI, with Sadio Mane and Naby Keita injured and Jordan Henderson a doubt.
Roberto Firmino is likely to start ahead of Daniel Sturridge in attack, while Xherdan Shaqiri could keep his place after impressing against the Terriers.
Five-time winners the Reds lost in the final last season and it was at home where they built their run.
Anfield has been a fortress in recent times, with them netting three or more in eight of their last nine outings and will be looking to take advantage of a side who are relative novices at this level.
Red Star are featuring in the group stages for the first time but have pedigree in European football, most notably being crowned European champions in 1991.
After that point against Napoli, their defeat in Paris was their joint-record European defeat and will have been a wake-up call.
That was, though, their first loss in 35 in all competitions and they have won their three competitive outings since.
Vladan Milojevic is likely to stick with his favoured XI and will be looking to channel the spirit of 1973, when The Star defeated Liverpool, the only time the pair have met.
There best source of goals is likely to come from Richmond Boakye, who has netted five in his last five and will be looking to continue a run that has helped his side strike in their last 10 on the road in all competitions.