The Blues progressed to a sixth semi-final in seven years with a scintillating 6-0 win over Burnley.
Sheffield United saw off Blackburn Rovers 3-2 at Bramall Lane to reach the last four.
City loanees Tommy Doyle and Jamie McAtee both played for United in the win over Rovers, with Doyle scoring the winning goal in stoppage time.
However, the pair won’t be eligible for the semi-final because loan players aren’t allowed to play against their parent clubs in the competition.
City and the Blades have played six matches previously in the FA Cup - with the Blues failing to win any!
The first meeting in 1906 ended in a 4-1 for the South Yorkshire side.
In 1914, the teams were paired again, with the first meeting ending 0-0 and the replay ending in the same score.
The Blades won the second replay 1-0.
In 1939, United again knocked City out, winning 2-0 at Bramall Lane and in 2008, the Blues were beaten 2-1 at the same venue - the infamous 'Balloongate' match when the hosts scored a goal that flew through a goal-mouth full of balloons released by the travelling City fans.
Manchester United or Fulham will face Brighton in the other semi.
The FA Cup semi-finals will be staged at Wembley Stadium across the weekend of Saturday 22 and Sunday 23 April.
Our fixture date will be confirmed on mancity.com and our official app shortly after the draw is made.
Ticket details will follow in due course.