Blackburn will take on Aston Villa in the other semi-final.
City knocked out Arsenal while United knocked out Tottenham in the quarter-finals.
Aston Villa overcam Portsmouth while Blackburn managed to beat favourites Chelsea on penalties.
Semi-final draw
Manchester City v Manchester United
Blackburn v Aston Villa
First legs to be played week commencing 4th January and second legs week commencing 18th January.
