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.