The other last four clash will see Watford take on Wolverhampton Wanderers, with both matches to take place on the weekend of April 6 and 7.
Pep Guardiola's side, who won the last of their five previous FA Cups in 2011, progressed to the semi-finals after staging a fine comeback to beat Championship side Swansea City .
Solly March's overhit free-kick beat Lions goalkeeper David Martin in stoppage time to draw the visitors level before the Seagulls prevailed 5-4 on spot-kicks after Jake Cooper's miss.
Manager Chris Hughton said: "All three teams didn't want to draw Man City but I think at this moment we are so pleased to go through and get to a semi-final. If we don't think we can win a semi-final there is no point going into it.
"We have an opportunity but we are up against at this moment with Liverpool the best team in the country and a team that is going for four competitions.
"On the day we will have a chance but we will have to get everything to go our way."
Watford will be seeking to reach the final of the world's oldest cup competition for just the second time after seeing off Crystal Palace in the first quarter-final of the weekend.
Andre Gray came off the bench to send the Hornets through and they will be looking to match their run to the final in 1984.
Wolves are four-time winners themselves but have not played in a final since 1960.
Indeed only 10 sides have played in more finals than the Molineux club, who produced the shock of the round to knock-out Manchester United.
FA Cup semi-final draw in full:
Watford vs Wolverhampton Wanderers
Manchester City vs Brighton and Hove Albion