Chelsea will be at home against the Premier League‘s bottom side Sheffield United after qualifying by beating Barnsley 1-0 on Thursday.
Championship side Bournemouth, who are currently looking for a new permanent manager, host south coast neighbours Southampton.
Everton wriggled their way into the last eight of the competition after coming through a nine-goal thriller against Tottenham on Wednesday, with Bernard’s extra-time winner giving them a 5-4 victory over Jose Mourinho’s side.
Pep Guardiola and his Manchester City side, meanwhile, made English football history by breaking the record for consecutive wins (15) in all competitions by a top-flight team as they beat Swansea 3-1 in the fifth round on Wednesday.
Everton haven’t played City this season after the original league fixture on December 23 was postponed due to a coronavirus outbreak in the City squad. The rearranged match, however, will take place on February 17.
Leicester had played United in the Premier League on Boxing Day last year and both sides could only settle for a 2-2 draw at the King Power.
Just two points currently separate the two sides in the league table after 23 games, with United ahead in second and Leicester third.
The quarter-finals are due to take place on the weekend of March 20-21.
FA Cup quarter-final draw:
- Everton vs Manchester City
- Bournemouth vs Southampton
- Leicester vs Manchester United
- Chelsea vs Sheffield United