The two English giants will fight for a place in the tournament's final against the winner of the other last-four fixture between Leicester City and Aston Villa.
Both Manchester sides got through to the semis against plucky lower league opposition, with the Red Devils grinding out a 3-0 win against League Two side Colchester United while Raheem Sterling's brace helped City to defeat League One club Oxford United 3-1
Leicster, meanwhile, required a penalty shootout to progress past Everton, as Jamie Vardy converted the winning spot-kick after Leighton Baines' dramatic stoppage-time equaliser ensured the match finished 2-2 at the end of 90 minutes.
Aston Villa booked their place in the last four on Tuesday with a comfortable 5-0 win against a Liverpool side weakened by those missing on Club World Cup duty.
The two English giants will fight for a place in the tournament's final against the winner of the other last-four fixture between Leicester City and Aston Villa.
Both Manchester sides got through to the semis against plucky lower league opposition, with the Red Devils grinding out a 3-0 win against League Two side Colchester United while Raheem Sterling's brace helped City to defeat League One club Oxford United 3-1
Leicster, meanwhile, required a penalty shootout to progress past Everton, as Jamie Vardy converted the winning spot-kick after Leighton Baines' dramatic stoppage-time equaliser ensured the match finished 2-2 at the end of 90 minutes.
Aston Villa booked their place in the last four on Tuesday with a comfortable 5-0 win against a Liverpool side weakened by those missing on Club World Cup duty.
United and Leicester will host the first legs of their ties in the week commencing January 6 with the return matches scheduled for the week beginning January 27.
Wembley Stadium will host the Carabao Cup final on March 1.
Manchester City will be aiming to win their third consecutive Carabao Cup title having defeated Arsenal 3-0 in 2018 and Chelsea on penalties after a goalless draw last season.
Pep Guardiola's side will also be seeking revenge after being beaten 2-1 by United in the Premier League at the Etihad Stadium on December 7.
Seeking a third consecutive Premier League titlel, City have fallen off the pace to be 14 points behind Liverpool after 17 matches.
The Red Devils, who have won five Carabao Cups in their history, are battling to get back into the top four and currently sit in sixth position, four points behind fourth-placed Chelsea.Leicester have been the Premier League's surprise package so far this term, with the Foxes currently sat in second position, albeit 10 points adrift of the Reds, and Brendan Rodgers' side will be hoping to win the Carabao Cup for the fourth time.
Aston Villa have won the tournament on five occasions, with the last coming in 1996 when they beat Leeds United in the final.
United and Leicester will host the first legs of their ties in the week commencing January 6 with the return matches scheduled for the week beginning January 27.
Wembley Stadium will host the Carabao Cup final on March 1.
Manchester City will be aiming to win their third consecutive Carabao Cup title having defeated Arsenal 3-0 in 2018 and Chelsea on penalties after a goalless draw last season.
Pep Guardiola's side will also be seeking revenge after being beaten 2-1 by United in the Premier League at the Etihad Stadium on December 7.
Seeking a third consecutive Premier League titlel, City have fallen off the pace to be 14 points behind Liverpool after 17 matches.
Leicester have been the Premier League's surprise package so far this term, with the Foxes currently sat in second position, albeit 10 points adrift of the Reds, and Brendan Rodgers' side will be hoping to win the Carabao Cup for the fourth time.
Aston Villa have won the tournament on five occasions, with the last coming in 1996 when they beat Leeds United in the final.