Liverpool will take on Stoke City for a place in the League Cup final, with Everton facing Manchester City in the other semi-final.
Jurgen Klopp's team stormed into the last four with a 6-1 triumph over Southampton at St Mary's - Belgium striker Divock Origi opening his Liverpool account with a hat-trick as Daniel Sturridge hit a brace on his first start since October - and they will travel to the Britannia Stadium in the first leg.
Manchester City head to Goodison Park first up and were in similarly emphatic mood as they brushed aside Hull City 4-1 at the Etihad Stadium on Tuesday night, where Origi's compatriot Kevin De Bruyne netted twice during the closing stages.
Stoke overcame Sheffield Wednesday 2-0 thanks to strikes from Ibrahim Afellay and Phil Bardsley, while Everton also beat Championship opposition by the same scoreline.
Gerard Deulofeu and Romelu Lukaku were on target for Roberto Martinez's men at Middlesbrough.
In 2014, Manchester City were League Cup winners, beating Sunderland 3-1 in the final, and Liverpool lifted the trophy two years earlier.
The 1972 League Cup remains as Stoke's only major honour and Everton will hope for the chance to go one better than being beaten finalists in 1977 and 1984 - the latter loss coming to their Merseyside rivals Liverpool.
The first legs of the ties will be played in the week commencing January 4, with the return matches scheduled for the week starting January 25.