United booked their place in the last four thanks to a 2-0 win over Stoke City at the Britannia Stadium, while Sunderland upset Chelsea 2-1 on Tuesday.
The draw leaves keeps alive the possibility of an all-Manchester final after City were pitted against West Ham United.
West Ham sealed their spot in the draw after they came from behind to seal a 2-1 win over Tottenham at White Hart Lane on Wednesday.
And Manuel Pellegrini’s City secured their last-four berth after a commanding 3-1 victory over Leicester on Tuesday night.
The first legs of the League Cup semi-final will be played on the week commencing 6 January 2014, with the return legs taking place in the week starting 20 January.
Sunderland v Manchester United
Manchester City v West Ham United
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news