United were pegged back to 2-2 by holders Chelsea at Old Trafford on Sunday, having led 2-0 at the break, while City demolished Barnsley 5-0 on Saturday thanks to a Carlos Tevez hat-trick.
The other semi will see Wigan, who hammered Everton 3-0 at Goodison Park on Saturday and will feature in the last four of the competition for the first time in their 81-year history, face either Millwall or Blackburn, who shared a goalless draw at The Den on Sunday.
City beat United 1-0 thanks to a Yaya Toure finish in the 2011 semis, with Paul Scholes sent off for a dangerous challenge.
City went on to beat Stoke 1-0 and lift their first trophy for 35 years. They followed it up with the Premier League the following year, but United seem certain to regain their league title this term as City trail them by 12 points with 10 games remaining.
Wigan chairman Dave Whelan might well be hoping Blackburn provide the opposition at Wembley which would be an emotional occasion for him.
He was in the Blackburn side that lost 3-0 to Wolverhampton Wanderers in 1960, the last time they reached the final, when he suffered a broken leg which effectively ended his playing career.
He later became a highly successful businessman, overseeing and sustaining Wigan's place in Premier League since they gaining promotion eight years ago.
The semi-finals will be played at Wembley on April 13 and 14 with the last-eight replays contested this Wednesday.