The Reds progressed to the last four with a 1-0 quarter-final victory over Nottingham Forest at the City Ground, courtesy of Diogo Jota's 78th-minute goal.
Jürgen Klopp's men will now take on Pep Guardiola's City in the next round after they eliminated Southampton earlier in the day.
Semi-final ties are scheduled to be played on April 16 and April 17. Confirmed fixture and ticket details will be announced in due course.