Liverpool and United will clash for two consecutive weekends with the top two also facing off in the Premier League on Sunday.
National League North side Chorley’s reward for their victory over a depleted Derby was a home tie with Premier League Wolves.
Chorley manager Jamie Vermiglio told BBC Sport: “That’s what we really wanted, Premier League opposition, great.
“And there’s a bit of history because in 1986, Chorley played against Wolves at home and beat them 3-0, so we just need to do that again.”
Should Chorley pull off another upset, they could face holders Arsenal in the fifth round.
League Two Crawley, who thrashed Leeds 3-0 in the third round, travel to Bournemouth.
The fourth round ties will be played across the weekend of January 22 to 25 with the fifth round taking place between February 9 to 11.
FA Cup fourth round draw:
Manchester United v Liverpool
Cheltenham v Manchester City
Bournemouth v Crawley
Swansea v Nottingham Forest
Southampton or Shrewsbury v Arsenal
Barnsley v Norwich
Chorley v Wolves
Millwall v Bristol City
Brighton v Blackpool
Wycombe v Tottenham
Fulham v Burnley
Sheffield United v Plymouth
Chelsea v Luton
Stockport or West Ham v Doncaster
Brentford v Leicester
Everton v Sheffield Wednesday
Fifth round draw:
Manchester United or Liverpool v Stockport/West Ham/Doncaster
Fulham or Burnley v Bournemouth or Crawley
Sheffied United or Plymouth v Millwall or Bristol City
Chorley or Wolves v Southampton/Shrewsbury/Arsenal
Barnsley or Norwich v Chelsea or Luton
Everton or Sheffield Wednesday v Wycombe or Tottenham
Swansea or Nottingham Forest v Cheltenham or Manchester City
Brentford or Leicester v Brighton or Blackpool.