United draw Liverpool in round four
United, who overcame City 3-2 at the Etihad Stadium, will face the Reds on the weekend of January 28 and 29.
United have won the competition 11 times, while Kenny Dalglish's men have triumphed on seven occasions.
QPR will host west London neighbours Chelsea if they can overcome the MK Dons in a replay at Loftus Road.
Chelsea captain John Terry could make a first return to the ground since he was accused of racially abusing Rangers defender Anton Ferdinand, a matter which has become the subject of a criminal case and an accusation which he strenuously denies.
As well as Liverpool versus Manchester United, there are two other definite all-Premier League ties with West Brom hosting Norwich and Everton welcoming Fulham to Goodison Park.
Arsenal will be at home to Aston Villa if they can overcome Leeds at the Emirates Stadium on Monday night, while Bolton will take on Swansea at the Reebok Stadium if they see off Macclesfield in a replay having drawn 2-2 at Moss Rose on Saturday.
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