Peterborough United will host either Leicester City, the Premier League champions of 2015-16, or Fleetwood Town in the fourth round of the FA Cup.
Top flight Leicester will be hot favourites to beat Fleetwood of League One in their third round replay on January 16. The sides drew 0-0 at Fleetwood on Saturday.
Posh have never played Leicester or Fleetwood in the FA Cup. They have met Leicester twice in the League Cup and lost both times, in a two-legged tie in 1992 and after a replay in 1965.
But Posh won the last meeting between the sides, a Championship fixture at London Road in 2013 when current manager Grant McCann scored an 88th minute winning goal in a 2-1 victory.
Posh have only ever beaten one top-flight side in the FA Cup, their famous win over Arsenal in a fourth round tie in 1965.
Posh won 3-2 at Fleetwood in a dramatic League One match in December.
Posh earned their place in the draw with an outstanding 3-1 success at Championship promotion hopefuls Aston Villa on Saturday (January 6).
The fourth round ties are scheduled for January 26-30. Posh will have to rearrange their League One match at Bury which was scheduled for January 27.
Full draw: Liverpool v West Brom, POSH v Leicester City of Fleetwood, Huddersfield v Birmingham, Notts County v Wolves or Swansea, Yeovil v Manchester United, Carlisle or Sheffield Wednesday v Stevenage or Reading, Cardiff or Mansfield v Manchester City, MK Dons v Coventry City, Millwall v Rochdale, Southampton v Watford, Middlesbrough v Brighton or Crystal Palace, Bournemouth or Wigan v Shrewsbury v West Ham, Hull v Nottingham Forest, Newport v Spurs, Norwich or Chelsea v Newcastle, Sheffield United v Preston.