Liverpool booked their place in the last four with a 2-0 victory over Chelsea while City won 1-0 at Arsenal.
The other Carling Cup semi-final tie will see Cardiff face Crystal Palace.
Carling Cup semi-final draw in full:
Manchester City v Liverpool
Crystal Palace v Cardiff
(First legs to be played in week commencing 9 January 2012, second legs to be played in week commencing 23 January 2012)
