United beat holders Chelsea 2-0 at Stamford Bridge earlier on Monday to book their spot in the last eight.
Crystal Palace were drawn away to Watford in another all-top-flight clash while second-tier Millwall host Brighton & Hove Albion in the other quarter-final.
Draw
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Swansea City v Manchester City
Watford v Crystal Palace
Wolverhampton Wanderers v Manchester United
Millwall v Brighton & Hove Albion
Ties to be played March 15-18
(Reporting by Karolos Grohmann)
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