Liverpool will face Manchester United in the FA Cup fourth round.
The winner of another fourth round tie involving West Ham or Stockport and Doncaster Rovers has then been scheduled to take place against the victor in the Reds' clash at Old Trafford.
The fifth round match would take place at Anfield.
Jurgen Klopp's men beat a young Aston Villa side 4-1 in the third round of the competition and secured progression after two goals from Sadio Mane and one each from Gini Wijnaldum and Mohamed Salah with teenager Louie Barry scoring for the hosts.
The fourth round ties are due to be played around the weekend of January 23/24, with the fifth round set to take place in midweek, on Wednesday, February 10.
It means, Liverpool will play Manchester United in consecutive weekends and the Reds have now been drawn against Premier League opposition 17 times in 26 domestic cup draws under Jurgen Klopp.
The Football Association announced that there would be a double draw on Monday, January 11, with the fourth-round draw immediately followed by the draw for the fifth round.
It marked a change in the traditional approach but was done to "aid fixture scheduling" in this most unusual of seasons, due to the ongoing coronavirus pandemic, and followed a similar organisation by the EFL in the Carabao Cup earlier this season.
Liverpool were allocated number 23 for the draw.
