The draw echoes the clash in 2017 when then Championship side Wolves pulled off a stunning 2-1 victory.
Richard Stearman and Andi Wiemann scored Wolves goals.
Wolves repeated the feat two years later, when they downed the Reds again in the Cup in 2019, this time at Molineux.
Raul Jimenez and Ruben Neves struck for Wolves on that occasion.
Wolves are currently bottom of the Premier League with Liverpool sitting sixth.
Premier League rivals Villa received a rare home draw where they will face minnows Stevenage, who currently sit second in League Two.
Albion will travel to non league Chesterfield, currently third in the National League, hoping to avoid a giant-killing.
Walsall will travel to Charlton or Stockport County after overcoming Carlisle in injury time last weekend.