United will face Burnley out of the home on 12 January while City will face Aston Villa on 20 January.
This two-match schedule was changed because European clubs from two big Manchester clubs played in the last round of the tournaments.
Manchester City qualified for the Champions League quarter-finals and lost 3–1 to Olympic Lyonesse on 15 August.
At the same time, United had met Sevilla in the semi-finals of the Europa League and also suffered a 1-2 defeat in the match played on 16 August. Sevilla later became the champion.