Manchester City, Manchester United and Chelsea were all handed away ties in the last eight of the competition.
The pick of the bunch sees the sole remaining Sky Bet Championship club in Leicester at home to Manuel Pellegrini's City.
City have not lifted the trophy since 1976 when they beat Newcastle 2-1, and it was the Magpies they despatched in the fourth round on Wednesday, albeit requiring extra-time goals from Alvaro Negredo and Edin Dzeko at St James' Park.
As for cross-city rivals United, boss David Moyes' side head to the Britannia Stadium for a clash with Stoke and one of three all-Premier League ties.
United only just edged former hero Mark Hughes' side 3-2 in the league at Old Trafford on Saturday, but the Potters will fancy their chances of revenge on home soil.
Chelsea, beaten semi-finalists last year, are also on the road, but will have to wait until next Wednesday to discover their opponents.
Jose Mourinho's side, covincing 2-0 winners at Arsenal on Tuesday, will head to either Sunderland or Southampton.
The final match-up is an all-London affair, but then only just as Spurs beat Hull 8-7 on penalties at White Hart Lane on Wednesday after a 2-2 draw at the end of 120 minutes.
Andre Villas-Boas has at least been rewarded with another home tie as they take on the Hammers, albeit with memories certain to still be fresh following a shock 3-0 home league defeat to Sam Allardyce's side on October 6.
Capital One Cup quarter-final draw
Leicester v Manchester City
Stoke v Manchester United
Sunderland or Southampton v Chelsea
Tottenham v West Ham
•Ties to be played week commencing December 16.