The Manchester clubs have been kept apart in the draw for the 6th round of the FA Cup.
Manchester United's quest for a thirteenth FA Cup win will continue with a quarter-final away to Brendan Rodgers' Leicester City.
Leicester will be hoping to make the semi-finals for the first time since 1982, when a young Gary Lineker started against his future employers Tottenham.
Manchester City will be away to Everton in round 6.
Everton secured their place with a dramatic 5-4 extra-time victory at home to Tottenham on Wednesday night. While City eased past Swansea City.
Southampton ended a run of four straight defeats with a 2-0 5th round win away to Wolves.
— Emirates FA Cup (@EmiratesFACup) February 11, 2021
Danny Ings beat the hosts' offside trap to put Ralph Hasenhüttl's side in front at Molineux, before Stuart Armstrong assured their progress with a late strike.
Southampton will make the short trip to English south-coast rivals Bournemouth in the quarter-finals.
The other 6th round tie will see the winners of the Barnsley-Chelsea tie entertaining the Premier League's bottom side Sheffield United.
FA Cup 6th round draw:
Everton v Manchester City
Bournemouth v Southampton
Leicester City v Manchester United
Barnsley or Chelsea v Sheffield United
Ties to be played the weekend of Saturday March 20