The English League Cup semi-final draw threw up a Manchester derby on Wednesday, with big-spending City to play holders United in January.
Blackburn Rovers, who beat league leaders Chelsea 4-3 on penalties after a 3-3 draw at the end of extra time, play Aston Villa.
The first leg matches will commence on the week beginning Jan. 4 with the second legs due to be played on the week commencing Jan. 18.
"We're just taking in the events of the evening so we're on a high at the moment, but I'm sure the whole of Manchester will be looking forward to those two games in the semi-final," City manager Mark Hughes told the BBC after his side beat Arsenal 3-0.
"We'd have fancied our chances against anyone in the draw so bring them on. We played really well tonight and ran out comfortable winners."