Holders Arsenal face a trip to either Southampton or Shrewsbury, while minnows Chorley face Premier League big guns Wolves
The two sides will meet in the Premier League on January 17, before meeting in the FA Cup a week later.
The FA took the decision to have the fourth and fifth round draws on the same day in order to aid with fixture scheduling on account of the condensed, coronavirus-affected season.
The fourth round ties will take place over the weekend of January 23, with the fifth round in the week of February 8.
Holders Arsenal required extra time before seeing off Newcastle to reach the fourth round and they will take on Southampton or Shrewsbury.
Manchester City lifted the trophy in 2019, and eased into the fourth round courtesy of a comfortable win over Birmingham and they face a trip to Cheltenham.
Liverpool lead the way in the Premier League, but have not won the FA Cup in 2006. They eased past a depleted Aston Villa side in round three to set up a clash with big rivals Manchester United who have started 2021 in style.
Chelsea snapped a poor run of form over the Christmas and New Year period by seeing off Morecambe to set up a meeting with Luton.
National League North side Chorley dumped Derby out of the competition and will meet Wolves in round four.
|Manchester United/ Liverpool||v||Stockport/West Ham or Doncaster|
|Sheffield United/Plymouth||v||Millwall/Bristol City|
|Swansea/Nott’m Forest||v||Cheltenham/Manchester City|