Late goals from Ilkay Gundogan and Kevin De Bruyne saw City past a dogged Everton 2-0 at Goodison Park on Sunday (AEDT), keeping the Premier League leader and Carabao Cup finalist in contention across four major competitions.
That result meant City has won 25 of its past 26 games in all competitions, with Chelsea similarly enjoying a rich vein of form.
The Blues are undefeated in 14 games under head coach Thomas Tuchel, with Hakim Ziyech – their midweek Champions League hero against Atletico Madrid – sealing a 2-0 win over Sheffield United on Sunday at Stamford Bridge.
The other semi-final will see the winner of the match between Leicester City and Manchester United take on Southampton
Ralph Hasenhuttl's men swept aside Championship outfit Bournemouth 3-0 on Saturday, with Nathan Redmond netting a second-half brace.
A tougher test likely awaits against United or Leicester, each of whom boast 9-0 wins against Saints over the past two seasons.
The ties will be played at Wembley on the weekend of April 17-18.
FA Cup semi-final draw in full:
Leicester City or Manchester United v Southampton
Chelsea v Manchester City