Just as the Reds and Hammers could not be separated at Upton Park, Saturday's Craven Cottage meeting between the Cottagers and the Seasiders ended all-square.
Both third round replays will take place in the week commencing Monday, 14 January, sandwiched between league fixtures at home to Liverpool and away to Tottenham Hotspur for United.
Elsewhere in the fourth round draw, there are no guaranteed all-Premier League ties. Stoke will host Manchester City if they overcome Crystal Palace, while Sunderland must beat Bolton if they are to face Everton, who travel to Cheltenham on Monday evening.
Full FA Cup fourth round draw
Norwich City v Luton Town, Oldham Athletic v Mansfield/Liverpool, Macclesfield Town v Wigan/Bournemouth, Derby County v Blackburn Rovers, Hull City/Leyton Orient v Barnsley, Middlesbrough v Aldershot Town, Millwall v Aston Villa, Leeds United/Birmingham City v Tottenham Hotspur, Brighton & Hove Albion v Swansea City/Arsenal, Crystal Palace/Stoke City v Manchester City, West Ham United/Manchester United v Fulham/Blackpool, Southend/Brentford v Chelsea, Reading v Sheffield United, Huddersfield Town v Leicester City, QPR/West Brom v Sheffield Wednesday/MK Dons, Bolton/Sunderland v Cheltenham/Everton