The Toffees were ball number 16 in the draw, which was shown live on BBC 2 from 7pm.
Everton have not won at Anfield since 1999, and travel to Jürgen Klopp’s Reds in the Premier League on Wednesday evening.
Liverpool are, of course, currently runaway leaders of the Premier League, having dropped just two points all season, and beat Everton in the same third round fixture two years ago thanks to a late header from debutant Virgil van Dijk.
Everton have won the competition five times in their 141-year history, but their FA Cup triumph over Manchester United in 1995 remains their most recent piece of silverware.
They reached the semi-finals in 2016, but have not made it past the fourth round in the three years since, suffering defeats to Leicester City, Liverpool and Millwall.
Here’s the full draw for the Third Round -
Arsenal v Leeds United
Birmingham v Blackburn
Bournemouth v Luton Town
Brentford v Stoke City
Brighton v Sheffield Wednesday
Bristol City v Shrewsbury
Bristol Rovers or Plymouth v Coventry or Ipswich
Burnley v Peterborough
Burton Albion v Northampton
Cardiff City v Forest Green Rovers or Carlisle
Charlton v West Brom
Chelsea v Nottingham Forest
Crystal Palace v Derby County
Eastleigh or Crewe v Barnsley
Fleetwood Town v Portsmouth
Fulham v Aston Villa
Gillingham v West Ham United
Leicester City v Wigan
Liverpool v Everton
Manchester City v Port Vale
Middlesbrough v Tottenham Hotspur
Millwall v Newport County
Oxford United v Exeter City or Hartlepool
Preston v Norwich City
QPR v Swansea City
Reading v Blackpool
Rochdale or Boston United v Newcastle United
Sheffield United v Fylde
Solihull Moors or Rotherham v Hull City
Southampton v Huddersfield
Watford v Tranmere
Wolverhampton Wanderers v Manchester United
Ties to be play on weekend 3-6 January