The Reds, who won the competition for the 12th and most recent time in 2016, will visit Wolves in the first weekend of January 2020, a few days after the midweek Premier League trip to Arsenal.
When the teams met at Molineux in the 2018/19 quarter-finals, the Midlands club triumphed 2-1. United had previously beaten Reading (2-0), Arsenal (3-1) and Chelsea (2-0) in the third, fourth and fifth rounds respectively.
In total, the two clubs have clashed nine times in the FA Cup with the Reds claiming four wins to Wolves' three, while two games have ended in draws.