Manchester United will host crosstown rivals City in the semifinals of the Carabao Cup, while Leicester are home to Aston Villa in the other semifinal.
The last-four ties will be played on Jan. 6 and Jan. 27.
United made the semifinals after beating Colchester 3-0, while holders went through with an easy win over Oxford United. United and City last met in the League Cup semifinals in 2010, when a late Wayne Rooney header gave Sir Alex Ferguson's side a memorable win.
Leicester and Everton provided the most drama of the three Wednesday matches, with the visitors blowing a two-goal lead before winning on penalties.
Leicester are in the League Cup semifinals for the first time since the 1999-2000 campaign, when they won the trophy.
Aston Villa were the first to qualify for the last four after beating the youngest Liverpool side in history 5-0 as the Reds senior team was away on Club World Cup duty in Qatar where they beat Monterrey to set up a finals showdown with Flamengo.