Jurgen Klopp’s side will take on Premier League opposition with the tie due to be played across the weekend of January 4-7.
Liverpool have failed to progress beyond the fourth round of the FA Cup since Klopp took charge at Anfield.
West Ham United, Wolverhampton Wanderers and West Bromwich Albion have dumped the Reds out at that stage of the competition across the last three seasons.
However, they enjoyed a rare high point before their habitual early exit last time out, claiming a dramatic 2-1 win over rivals Everton in the third round.
Virgil van Dijk marked his debut for the club by rising highest to meet a corner at the Kop end in the final moments of a hard-fought tie against the Toffees.
Klopp's men were subsequently handed another home draw, this time against West Brom, but put in one of their poorest performances of the season in going out.
Jay Rodriguez scored twice in a shock 3-2 victory for the Baggies, despite the hosts having led after just five minutes through Roberto Firmino.
