Ole Gunnar Solskjaer's men will face the Foxes on Sunday 21 March at 17:00 GMT, a match UK residents will be able to watch on BBC Sport.
The Reds made it to the last eight by eliminating Watford, Liverpool and West Ham United, and a victory over Leicester would see us reach the semi-finals for the second season in a row.
FA CUP QUARTER-FINALS IN FULL
SATURDAY 20 MARCH
Bournemouth v Southampton (12:15 GMT on BT Sport)
Everton v Manchester City (17:30 GMT on BT Sport)
SUNDAY 21 MARCH
Chelsea v Sheffield United (13:30 GMT on BBC One)
Leicester City v United (17:00 GMT on BBC One)