The Reds will play the second Merseyside derby of the season as they look to improve on last season’s fourth-round exit with a successful cup run in 2018.
Both of Klopp’s previous FA Cup third round games have required replays, and both previous seasons his Liverpool side have exited at the fourth round stage.
This will be the 23rd time Liverpool have played their city rivals in the FA Cup in their history, with their last meeting in the tournament coming in the semi-final in 2012.
Dalglish resigned after a 4-4 draw with the Toffees in the FA Cup fifth round in his first stint in charge of Liverpool in 1991.
The Reds and Blues face each other this Sunday afternoon in the Premier League, as Klopp takes on an old adversary in Sam Allardyce.
Everton are currently 10th in the league, with Allardyce winning his first game in charge on Saturday, a 2-0 victory at home to Huddersfield Town.
FA Cup 3rd Round Draw
- Ipswich vs. Sheffield United
- Watford vs. Bristol City
- Birmingham vs. Burton Albion
- LIVERPOOL vs. Everton
- Aston Villa vs. Woking/Peterborough
- Bournemouth vs. Fylde/Wigan
- Coventry vs. Stoke
- Newport vs. Leeds
- Bolton vs. Huddersfield
- Port Vale/Yeovil vs. Bradford
- Brentford vs. Notts County
- QPR vs. MK Dons
- Man United vs. Derby
- Forest Green/Exeter vs. West Brom
- Doncaster vs. Slough/Rochdale
- Tottenham vs. AFC Wimbledon
- Fleetwood/Hereford vs. Leicester
- Blackburn/Crewe vs. Hull
- Cardiff vs. Mansfield
- Shrewsbury vs. West Ham
- Wolves vs. Swansea
- Stevenage vs. Reading
- Newcastle vs. Luton
- Millwall vs. Barnsley
- Wycombe vs. Preston
- Gillingham/Carlisle vs. Sheffield Wednesday
* Ties to be played on January 5-8.