The Red Devils will make the trip to Anfield, having knocked out holders and rivals Manchester City in round three earlier today.
Elsewhere, Sunderland face a home tie with North East rivals Middlesbrough, while Newcastle United will travel to either Brighton & Hove Albion or Wrexham.
FA Cup round four draw in full:
Brighton or Wrexham vs. Newcastle United
Sunderland vs. Middlesbrough
Dagenham or Millwall vs. Southampton
Hull City vs. Crawley Town
MK Dons or QPR vs. Chelsea
West Bromwich Albion vs. Norwich City
Blackpool vs. Sheffield Wednesday
Arsenal or Leeds vs. Aston Villa
Stevenage vs. Notts County
Watford vs. Tottenham Hotspur
Liverpool vs. Manchester United
Derby County vs. Stoke City
Everton vs. Fulham
Macclesfield or Bolton Wanderers vs. Swansea City
Sheffield United vs. Birmingham City or Wolverhampton Wanderers
Nottingham Forest or Leicester City vs. Swindon Town
Ties to be played on the weekend starting Saturday, January 28.