Monday’s draw for the last eight also handed Chelsea a home tie against League One giant-killers Port Vale, who stunned Sunderland with a 1-0 win in the fifth round on Sunday.
West Ham or Brentford, who meet on Monday, will host Leeds in the other quarter-final.
But it is City’s latest showdown with rivals Liverpool that is the stand-out tie of the round.
Pep Guardiola’s side have already beaten Liverpool twice this season, winning 3-0 in Manchester in November and earning a 2-1 victory at Anfield in February.
It will be the first FA Cup meeting between the clubs since Liverpool won 3-2 in the semi-finals in 2022.
Liverpool, 3-1 winners at Wolves in the last 16, have won the FA Cup eight times, most recently four years ago.
Seven-time winners City, who beat Newcastle 3-1 in the fifth round, last lifted the trophy in 2023.
Premier League leaders Arsenal advanced to the quarter-finals with a 2-1 win at third tier Mansfield.
Mikel Arteta’s men will head to Championship play-off hopefuls Southampton, who enjoyed a surprise 1-0 win at Fulham in the fifth round.
Quarter-final draw:
- Southampton v Arsenal
- Chelsea v Port Vale
- Manchester City v Liverpool
- West Ham or Brentford v Leeds
Ties to be played around the weekend of April 4-5.