Jurgen Klopp's men will play hosts to Sam Allardyce's charges at Anfield in the biggest encounter of the round.
Defending champions Arsenal will take on Championship outfit Nottingham Forrest, while Manchester United and Chelsea also face second tier sides in Derby County and Norwich City respectively.
Manchester City, who lost to Arsenal in the semi-finals last season, will host Burnley at the Etihad.
The third round matches will be played across the weekend of the 5th-8th of January 2018.
Ipswich Town v Sheffield United
Watford v Bristol City
Birmingham City v Burton Albion
Liverpool v Everton
Brighton v Crystal Palace
Aston Villa v Woking/Peterborough United
Bournemouth v AFC Fylde/Wigan
Coventry City v Stoke City
Newport County v Leeds United
Bolton Wanderers v Huddersfield Town
Port Vale/Yeovil Town v Bradford City
Nottingham Forrest v Arsenal
Brentford v Notts County
QPR v MK Dons
Manchester United v Derby County
Forrest Green Rovers/Exeter City v West Bromwich Albion
Doncaster Rovers v Slough Town/Rochdale
Tottenham Hotspur v AFC Wimbledon
Middlesbrough v Sunderland
Fleetwood Town/Hereford v Leicester City
Blackburn Rovers/Crew Alexandra v Hull City
Cardiff City v Mansfield Town
Manchester City v Burnley
Shrewsbury Town v West Ham United
Wolves v Swansea City
Stevenage v Reading
Newcastle United v Luton Town
Millwall v Barnsley
Fulham v Southampton
Wycombe Wanderers v Preston North End
Norwich City v Chelsea
Gillingham/Carlisle United v Sheffield Wednesday