Havant & Waterlooville could be rewarded with a trip to Anfield to face Liverpool if the Blue Square South minnows beat Swansea City in a replay after drawing 1-1 at the weekend.
They play at home to Roberto Martinez's side a week tomorrow, while Rafael Benitez's side must overcome Luton Town to reach the last 32.
The Hawks' manager, Shaun Gale, is refusing to get carried away. "It's fantastic. We've got a tough tie getting past Swansea, I'm sure they'll want to go there [Anfield] as well," he told Sky Sports News.
There are two all-Premier League ties, with Manchester United at home to Tottenham Hotpsur or Reading, and Wigan Athletic at home to the FA Cup holders Chelsea.
Newcastle United could face the League leaders Arsenal twice in four days.
The Magpies, who travel to the Emirates Stadium in the Premier League on 29 January will also face Arsne Wenger's side the previous weekend if they manage to see off Stoke in their third-round replay next week.
If West Ham overcome Manchester City in their replay then it would set up a potentially explosive clash with Sheffield United at Bramall Lane. The Blades still harbour ill feeling towards the Hammers and feel it should have been the London club who were relegated to the Championship last season for fielding ineligible player Carlos Tevez.
The Oldham manager, John Sheridan, was disappointed to be drawn against Huddersfield and Latics legend Andy Ritchie after their teams' heroics against Everton and Birmingham City respectively.
"I'm a good friend of Andy and I'm sure he'll be disappointed. It'll be a full house and a game we both think we can win," he said.
FA Cup fourth-round draw
Arsenal v Stoke City or Newcastle United
Coventry City v Walsall or Millwall
Oldham v Huddersfield
Swindon or Barnet v Fulham or Bristol Rovers
Wigan Athletic v Chelsea
Luton or Liverpool v Swansea or Havant & Waterlooville
Southend United v Barnsley
Southampton v Norwich City or Bury
Manchester United v Tottenham Hotspur or Reading
Portsmouth v Plymouth
Derby County or Sheffield Wednesday v Preston
Watford v Wolverhampton
Peterborough v Charlton or West Bromwich
Sheffield United v West Ham United or Manchester City
Mansfield v Middlesbrough
Tranmere or Hereford v Cardiff City
Ties to be played on weekend of 26-27 January.Reuse content