League Cup last eight draw
In the other all-Premier League tie drawn on Saturday, Arsenal will host Wigan Athletic.
Arsenal manager Arsene Wenger has often used the competition to try out youngsters in the past but he has been fielding stronger teams this season in a bid to win the club's first trophy in five years.
Ipswich Town manager Roy Keane, the former Manchester United captain, missed out on a match against his old club when the Championship side were drawn at home to West Bromwich Albion.
The tie evokes memories of the 1978 FA Cup semi-final when bloodied Albion captain John Wile carried on playing against Ipswich despite a bad headwound.
Last season's beaten finalists Villa travel to arch rivals Birmingham hoping to go one better in the competition this year.
New Villa manager Gerard Houllier has a good League Cup pedigree, having won the competition twice with Liverpool in 2001 and 2003.
The ties will be played in the weeks starting November 29 and December 6.