David Moyes’ Red Devils booked their place in the last eight thanks to a convincing 4-0 win over Norwich City on Tuesday, while Stoke were winners on penalties against Birmingham.
Tottenham, meanwhile, will host London rivals West Ham United after Andre Villas-Boas’ men sealed a dramatic penalty shootout triumph over Hull City on Wednesday following a 2-2 draw at White Hart Lane.
Elsewhere, Manchester City will travel to Championship high-flyers Leicester, and either Sunderland or Southampton will host Chelsea.
All of the quarter-final ties will be played in the week commencing 16 December 2013.
Stoke City v Manchester United
Leicester City v Manchester City
Sunderland or Southampton v Chelsea
Tottenham v West Ham United
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