Jurgen Klopp's side will travel back to Villa Park on the weekend of January 9-10, having been convincingly beaten at the ground in the Premier League in early October.
With replays scrapped for this year's tournament, the game will be decided on the night: with extra-time and penalties if required.
The tie is sandwiched between Manchester City's visit of Anfield on January 6th and Liverpool's trip to the King Power Stadium on January 13th. Klopp is therefore expected to name another heavily rotated side.
It is the fourth consecutive season where Liverpool have had to face a fellow Premier League team in the third round.
The Reds haven't fared well in the competition under Klopp and have only gone so far as to make it to the fifth round, as they did last year with a 2-0 defeat against Chelsea.
Full FA Cup Third Round Draw
Huddersfield Town vs Plymouth Argyle
Southampton vs Shrewsbury
Chorley vs Derby County
Marine vs Tottenham
Wolves vs Crystal Palace
Stockport County vs West Ham
Oldham Athletic vs AFC Bournemouth
Manchester United vs Watford
Stevenage vs Swansea City
Everton vs Rotherham United
Nottingham Forest vs Cardiff City
Arsenal vs Newcastle United
Barnsley vs Tranmere Rovers
Bristol Rovers vs Sheffield United
Canvey Island/Boreham Wood vs Millwall
Blackburn Rovers vs Doncaster Rovers
Stoke City vs Leicester City
Wycombe Wanderers vs Preston North End
Crawley Town vs Leeds United
Burnley vs MK Dons
Bristol City vs Portsmouth
QPR vs Fulham
Aston Villa vs Liverpool
Brentford vs Middlesbrough
Manchester City vs Birmingham City
Luton Town vs Reading
Chelsea vs Morecambe
Exeter City vs Sheffield Wednesday
Norwich City vs Coventry City
Blackpool vs West Brom
Newport County vs Brighton
Cheltenham Town vs Mansfield Town