Jurgen Klopp's side will take on their arch rivals in the fourth round having beaten Aston Villa 4-1 on Friday evening.
The fixture falls between the Reds' clash against Burnley on January 21 and a trip to the Tottenham Hostpur Stadium on January 28.
The fifth round draw also took place on Monday, with the winners facing an easier opponent in the next round in either Stockport County, West Ham or Doncaster Rovers on February 10/11
The two sides - who are currently top of the Premier League table and face eachother this weekend - last met in the FA Cup in 2012, with the Reds progressing at Anfield after a late strike by Dirk Kuyt after Ji-sung Park had cancelled out Daniel Agger's opener.
They last met in a cup competition in 2012, with Klopp's side knocking United out of the Europa League in the round of 16, with Daniel Sturridge, Roberto Firmino and Philippe Coutinho scoring across the two legs.
While the likes of Gini Wijnaldum insisted the Reds would like to go far in the competition, Old Trafford remains a tricky venue, particularly considering Liverpool's record in the FA Cup under Klopp.
Liverpool last won the FA Cup over 14 years ago, having been beaten in the semi-finals and finals twice in the previous decade.
4th/5th Round Draws in Full
Cheltenham Town v Manchester City
Bournemouth v Crawley Town
Swansea City v Nottingham Forest
Manchester United v Liverpool
Southampton or Shrewsbury Town v Arsenal
Barnsley v Norwich City
Chorley v Wolverhampton Wanderers
Millwall v Bristol City
Brighton and Hove Albion v Blackpool
Wycombe Wanderers v Tottenham Hotspur
Fulham v Burnley
Sheffield United v Plymouth Argyle
Chelsea v Luton Town
Stockport County or West Ham United v Doncaster Rovers
Brentford v Leicester City
Everton v Sheffield Wednesday
Fulham or Burnley will play Bournemouth or Crawley
Manchester United or Liverpool v Stockport County or West Ham or Doncaster Rovers
Sheffield United or Plymouth Argyle v Millwall or Bristol City
Chorley or Wolves v Southampton or Shrewsbury Town or Arsenal
Barnsley or Norwich City v Chelsea or Luton Town
Everton or Sheffield Wednesday v Wycombe Wanderers or Tottenham Hotspur
Swansea or Nottingham Forest v Cheltenham or Manchester City
Brentford or Leicester v Brighton or Blackpool