Everton will battle City to Goodison Park for the first of their two-legged tie, while Stoke are at home first against Liverpool.
The first legs will be played over 5 and 6 January, with the return matches played on 26 and 27 January.
Liverpool won 6-1 at Southampton in Wednesday’s only quarter-final, while City beat Hull 4-1 on Tuesday.
Everton won 2-0 at Middlesbrough in the previous round, while Stoke beat Championship opposition in Sheffield Wednesday, winning 2-0 at home.
After his team thrashed Saints, Reds boss Jurgen Klopp said: “I’ve had a few finals in my life and I know there was never an easy one. Stoke will want this final, for sure.”
Support InfoStride News' Credible Journalism: Only credible journalism can guarantee a fair, accountable and transparent society, including democracy and government. It involves a lot of efforts and money. We need your support. Click here to Donate