The Reds' reward for seeing off Aston Villa is a fourth-round clash with the Championship side, who have been rejuvenated since the arrival of Chris Wilder as manager.
The decision to show the game in the Friday night slot, with a 20:00 GMT kick-off, means the victors on the evening will be the first to take up a place in the draw for round five, with extra-time and penalties determining the result if the match is tied after 90 minutes, rather than a replay.
The Old Trafford encounter will be screened live on ITV in England, with the broadcaster also covering Tottenham versus Brighton (Saturday 20:00 GMT), Liverpool's home game with Cardiff City (Sunday, 12:00 GMT) and Boreham Wood's trip to Bournemouth (Monday, 18:30 GMT).