Draw also produces another Second City derby
In-form Arsenal have been given a home tie against Roberto Martinez's Wigan, while the tie of the round is Birmingham hosting rivals Aston Villa at St Andrew's.
Ipswich Town, the only Championship club in the last eight, host West Brom who have made a fantastic start to the season under Roberto Di Matteo.
Holders United, who overcame Wolves in the last round thanks to Javier Hernandez's last-gasp goal, will be delighted to have avoided rivals Arsenal and will be confident of progressing after enjoying this competition in recent seasons.
West Ham beat Stoke City 3-1 in the last round and have enjoyed this year's League Cup run after finding themselves bottom in the league.
Wigan face a daunting trip to the Emirates Stadium as Arsenal continue their push to end five seasons without a trophy.
It is a repeat of the fourth round fixture in 2008-09 which Arsenal won 3-0 with an experimental line-up.
But this season Arsene Wenger has changed his philosophy on the competition and has fielded relatively strong line-ups in the previous two rounds against Tottenham and Newcastle.
If Aston Villa are to repeat last season's trip to Wembley this term they will have to do it the hard way by winning a visit to St Andrew's against arch-rivals Birmingham.
Gerard Houllier has fond memories of the League Cup, winning it in 2001 with Liverpool; but Birmingham will be hoping to end Villa's dominance in the derby matches by reversing a six-game losing streak.
Meanwhile, high-flying West Brom face a tricky trip to Roy Keane's Ipswich.
The former Manchetser United captain will be relishing the chance to take on higher opposition and will be looking to get to Wembley for the first time as a manager.