The two sides have met before, back in 1973, when the then Yugoslavian outfit beat Bill Shankly's Reds in both legs of a European Cup tie.
Fortunes have changed for each team since then, with eight-time finalists Liverpool going on to win the competition on five occasions.
Red Star lifted the European Cup in 1991 but, until this year, had not qualified for the group stages of the tournament since its rebrand to the Champions League the following year.
Now back at the top table, the Serbian Super Liga winners held Carlo Ancelotti's Napoli to a 0-0 draw in their Group C opener in Belgrade last month but were then beaten 6-1 at Paris Saint-Germain.