The two Merseyside clubs face each other for the first time this season on Sunday in the Premier League.
But it’ll be red versus blue once again less than a month later as Liverpool welcome Sam Allardyce’s side to Anfield.
Brighton have also been drawn against Crystal Palace in another clash between two rivals.
Manchester City host Burnley in an all-Premier League clash, while Manchester United take on Championship Derby, as AFC Wimbledon go to Wembley to face Tottenham.
Arsenal take on Nottingham Forest as Chelsea visit Championship side Norwich.
Ties will be played over the 5-6 January with selected matches shown on TV.
FULL FA CUP THIRD ROUND DRAW BELOW
Gillingham or Carlisle vs Sheffield Wednesday
Norwich City vs Chelsea
Wycombe Wanderers vs Preston North End
Fulham vs Southampton
Millwall vs Barnsley
Newcastle vs Luton Town
Stevenage vs Reading
Wolves vs Swansea
Shrewsbury Town vs West Ham
Manchester City vs Burnley
Cardiff vs Mansfield Town
Blackurn or Crewe vs Hull
Fleetwood Town or Hereford vs Leicester
Middlesbrough vs Sunderland
Tottenham vs AFC Wimbledon
Doncaster Rovers vs Slough Town or Rochdale
Forest Green Rovers or Exeter City vs West Brom
Manchester United vs Derby County
QPR vs MK Dons
Brentford vs Notts County
Nottingham Forest vs Arsenal
Port Vale or Yeovil vs Bradford City
Bolton vs Huddersfield
Newport County vs Leeds
Coventry vs Stoke City
Bournemouth AfC Fylde or WIgan
Aston Villa vs Woking or Peterborough
Brighton vs Crystal Palace
Liverpool vs Everton
Birmingham City vs Burton Albion
Watford vs Bristol City
Ipswich vs Sheffield United