The Toffees beat Tottenham Hotspurs 5-4 in aclassic tie to reach the last eight.
The match at the King Power Stadium sees the top-flight’s third-placed side host the team in second.
In the other ties, Bournemouth play Southampton in a south coast derby while Barnsley or Chelsea will host Sheffield United.
Saints booked their place in the quarter-finals with an impressive 2-0 win at Wolves.
Only Championship side Barnsley can prevent the last eight being comprised entirely of top-flight sides when they host Thomas Tuchel’s Chelsea, also on Thursday.
The ties are scheduled to take place over the weekend of 20 and 21 March.
Full quarter-final draw:
Everton v Manchester City
Bournemouth v Southampton
Leicester City v Manchester United
Barnsley or Chelsea v Sheffield United
Credit: BBC Sports
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