The draw for the third round of the competition was made at Wembley on Sunday by Fabrice Muamba and Ledley King.
Two non-league sides must fight it out for the right to host Liverpool.
Lincoln and Mansfield drew 3-3 at Sincil Bank on Saturday and the replay will carry the bounty of a lucrative home meeting with Brendan Rodgers' men.
Rafael Benitez's Chelsea will begin their defence of the trophy with a tough-looking all-Premier League tie at St Mary's.
The two sides have yet to meet in the league this season and last met in the FA Cup in 1977 when Saints knocked out the Blues in a third-round replay.
Perhaps the most attractive third-round tie, though, sends Manchester United to West Ham.
Sir Alex Ferguson's 11-time winners beat the Hammers 1-0 in the league last week, but the two have enjoyed some memorable cup battles over the years, including when Paolo Di Canio scored the only goal of a surprise 1-0 West Ham win in 2001.
Premier League champions Manchester City host Gianfranco Zola's Watford, while Arsenal, whose last trophy was the 2005 FA Cup, must head to Swansea, the side who sent them off their own field to a chorus of boos with a 2-0 win on Saturday.
There is a tie for the nostalgics at White Hart Lane where Tottenham have been paired with Coventry, evoking memories of City's famous 3-2 final win over Spurs in 1987.
Everton face would-be giant-killers in the form of Cheltenham or Hereford, who play on Monday.
Elsewhere for the Premier League sides, 2011 finalists Stoke head to Championship leaders Crystal Palace, Newcastle travel to Brighton who beat them last season, and Fulham are at home to Blackpool.
Seven-time winners Aston Villa welcome Ipswich to the midlands, Bournemouth travel to Wigan and Reading go to Crawley, whose director of football is former Royals boss Steve Coppell.
Bottom-of-the-table QPR lock horns with West Brom, Norwich go to Championship strugglers Peterborough and 1973 winners Sunderland are at Bolton.
Hastings United, the lowest-ranked team left, have the lure of a trip to Middlesbrough if they beat Harrogate Town in a replay, while Barrow or Macclesfield will be at home to Cardiff.
The other games put Charlton up against Huddersfield, Barnsley against Burnley, Leicester against Burton and Millwall against Preston.
League One leaders Tranmere go to Derby, Aldershot face Rotherham or Notts County, Sheffield United head to Accrington or Oxford and Nottingham Forest play Oldham.
Hull boss Steve Bruce, a winner with Manchester United, will host Leyton Orient, Blackburn meet Bristol City, Leeds and Birmingham lock horns, Bury or Southend meet Bradford or Brentford, Wolves go to Luton and finally, MK Dons go to Sheffield Wednesday after beating AFC Wimbledon 2-1.
FA Cup third-round draw in full:
Crystal Palace v Stoke, Brighton v Newcastle, Tottenham v Coventry, Wigan v Bournemouth, Fulham v Blackpool, Aston Villa v Ipswich, Charlton v Huddersfield, Barrow or Macclesfield v Cardiff, Barnsley v Burnley, Manchester City v Watford, Swansea v Arsenal, Leicester v Burton Albion, Millwall v Preston, Cheltenham Town or Hereford United v Everton, Derby v Tranmere, Crawley v Reading, Aldershot v Rotherham or Notts County, Middlesbrough v Harrogate Town or Hastings United, Accrington or Oxford United v Sheffield United, Southampton v Chelsea, QPR v West Brom, Peterborough v Norwich, Lincoln City or Mansfield v Liverpool, Bolton v Sunderland, Nottingham Forest v Oldham, West Ham v Manchester United, Hull City v Leyton Orient, Blackburn v Bristol City, Leeds United v Birmingham, Bury or Southend v Bradford or Brentford, Luton v Wolves, Sheffield Wednesday v MK Dons.
Ties to be played over the weekend of 5 and 6 January, 2013.