League One Shrewsbury could host European champions Liverpool in the FA Cup fourth round later this month as holders Manchester City take on Fulham.
The Shrews host Bristol City in a third round replay next week with the winners earning the right to take on the runaway Premier League leaders.
Chelsea also face lower league opposition as Frank Lampard’s men travel to Championship side Hull.
Manchester United and Tottenham could have a trip to Premier League opposition to contend with should they come through replays.
United must overcome Wolves at home on January 14 for the right to face either Watford or League One Tranmere Rovers.
Spurs will travel to Southampton, where they lost on New Years’ Day, if they beat Middlesbrough.
The winners of Monday”s meeting between Arsenal face a trip to Bournemouth.
League Two Northampton, the lowest side in the English football pyramid sure of their place in the last 32, host Wayne Rooney’s Derby.
Draw in full:
Watford or Tranmere v Wolves or Manchester United
Hull v Chelsea
Southampton v Middlesbrough or Tottenham
QPR v Sheffield Wednesday
Bournemouth v Arsenal
Northampton v Derby
Brentford v Leicester
Millwall v Sheffield United
Reading or Blackpool v Cardiff or Carlisle
West Ham v West Brom
Burnley v Norwich
Bristol Rovers or Coventry v Birmingham
Manchester City v Fulham
Rochdale or Newcastle v Oxford
Portsmouth v Barnsley
Bristol City or Shrewsbury v Liverpool
Ties to be played over the weekend of January 24-27.