FA Cup holders Chelsea have been handed a fourth round trip to Wigan Athletic, while the draw also raised the prospect of Havant & Waterlooville travelling to Anfield to face Liverpool.
The non-league Hawks have to overcome Swansea City in a replay to have a chance of taking on Rafa Benitez's side, who have to see off Luton Town in a replay of their own.
Giant-killers Oldham Athletic and Huddersfield Town will meet at Boundary Park, while League Two strugglers Mansfield Town will host Middlesbrough at Field Mill.
Fourth round draw:
Arsenal v Stoke City or Newcastle United
Coventry City v Walsall or Millwall
Oldham Athletic v Huddersfield Town
Swindon Town or Barnet v Fulham or Bristol Rovers
Wigan Athletic v Chelsea
Luton Town or Liverpool v Swansea City or Havant & Waterlooville
Southend United v Barnsley
Southampton v Norwich City or Bury
Manchester United v Tottenham Hotspur or Reading
Portsmouth v Plymouth Argyle
Derby County or Sheffield Wednesday v Preston North End
Watford v Wolves
Peterborough United v Charlton Athletic or West Brom
Sheffield United v West Ham or Manchester City
Mansfield Town v Middlesbrough
Tranmere Rovers or Hereford United v Cardiff City
Ties to be played on the weekend of January 26 & 27.