The two rivals, currently first- and second-placed in the Premier League, will face off on Sunday 24 January at 5pm, with the meeting at Old Trafford set to air live on BBC One. The remaining fixtures in the round will be played on the same weekend.
United defeated Championship outfit Watford 1-0 in the third round, while Liverpool saw off an Aston Villa side comprising youth players 4-1 after a coronavirus outbreak at the club.
In the fifth round, the winner of United vs Liverpool will play the victor from West Ham and Doncaster’s fourth-round tie.
Below is the FA Cup fourth-round schedule in full (all times GMT).
Friday 22 January
Chorley vs Wolves – 7.45pm – BT Sport 1
Saturday 23 January
Southampton/Shrewsbury vs Arsenal – 12.15pm – BT Sport 1
Bournemouth vs Crawley – 3pm – BT digital platforms
West Ham vs Doncaster – 3pm – BBC digital platforms
Sheffield United vs Plymouth Argyle – 3pm – BBC digital platforms
Brighton vs Blackpool – 3pm – BT digital platforms
Barnsley vs Norwich – 3pm – BT digital platforms
Millwall vs Bristol City – 3pm – BT digital platforms
Swansea vs Nottingham Forest – 3pm – BT digital platforms
Cheltenham vs Man City – 17.30pm – BBC One
Sunday 24 January
Chelsea vs Luton – 12pm – BBC One
Brentford vs Leicester – 2.30pm – BT Sport 1
Fulham vs Burnley – 2.30pm – BT Sport digital platforms
Man United vs Liverpool – 5pm – BBC One
Everton vs Sheffield Wednesday – 8pm – BT Sport 1
Monday 25 January
Wycombe Wanderers vs Tottenham – 7.45pm – BT Sport 1