Louis van Gaal's men overcame League One opposition Yeovil Town in the third round on Sunday and they will come up against fourth-tier opposition in Cambridge in their next tie.
Cambridge overcame Luton Town 2-1 in their third-round clash on Saturday and Richard Money's men, who were promoted via the Conference play-offs last season, will now have the chance to take on the Van Gaal's expensively assembled Premier League squad.
Holders Arsenal, who defeated Hull City 2-0 in a re-run of last year's final in the third round at the weekend, will travel to Championship outfit Brighton and Hove Albion.
Top-flight leaders Chelsea have been given a home tie against either Millwall or Bradford City, who drew 3-3 in an entertaining encounter first time round.
Meanwhile Manchester City, who had to come from behind to see off Sheffield Wednesday in the last round, have been given another home tie against Championship opposition in Middlesbrough.
The ties will be played on the weekend of January 24 and 25.
Draw in full:
Crystal Palace v Southampton or Ipswich Town
Cambridge United v Manchester United
Blackburn Rovers v Swansea City
Chelsea v Millwall or Bradford City
Derby County v Scunthorpe United or Chesterfield
Preston North End v Sheffield United
Birmingham City v West Brom
Aston Villa v AFC Bournemouth
Cardiff City v Reading
AFC Wimbledon or Liverpool v Bolton Wanderers
Burnley or Tottenham Hotspur v Leicester City
Brighton and Hove Albion v Arsenal
Rochdale v Stoke City
Sunderland v Fulham or Wolverhampton Wanderers
Doncaster Rovers or Bristol City v Everton or West Ham
Manchester City v Middlesbrough
