The Red Devils will take on the Championship outfit in the quarter-finals, while Arsenal will host West Ham and Chelsea will face Bournemouth
Holders Manchester United will travel to Bristol City in the quarter-finals of the Carabao Cup.
United, who defeated Swansea City 2-0 in the fourth round, will head to Ashton Gate to take on the Championship side, who downed Crystal Palace 4-1 in the previous round.
Red Devils 3/1 for the cup
Elsewhere in the draw, which was delayed on two occasions due to a technical problem involving Twitter, Chelsea were drawn against Bournemouth while Arsenal were paired with West Ham.
Five-time winners Chelsea secured their place in the last eight by defeating Everton 2-1 in the fourth round, whereas Bournemouth got the better of Middlesbrough in a 3-1 victory.
Arsenal fought back from a goal down to beat Norwich City 2-1 thanks to a double from youngster Eddie Nketiah last time out, whereas the Hammers also came from behind to beat Tottenham 3-2.
Spurs led 2-0 thanks to goals from Moussa Sissoko and Dele Alli, but an Andre Ayew brace and a goal from Angelo Ogbonna completed an incredible turnaround for West Ham.
Leicester City were also paired with Pep Guardiola's high-flying Manchester City in the quarter-final draw on Thursday.
Full draw below:
Chelsea vs. Bournemouth
Arsenal vs. West Ham
Leicester City vs. Manchester City
Bristol City vs. Manchester United