We’ll play the League One side in the week commencing 14 December, with the exact fixture details to be confirmed in the coming days.
We reached the last eight of the competition with a dramatic 4-3 penalty shootout victory over Brighton at home on Wednesday night.
That followed a 2-2 draw in 90 minutes, which saw us twice come from behind thanks to goals from Mateo Kovačić and Vitor Reis.
Enzo Maresca’s side had previously overcome Norwich City, beating the Championship side 5-0 in September.
It means we remain in with a chance of defending our trophy won at Wembley last March.
Success in the competition this season would be our 10th in the League Cup’s history and see us draw level with record winners Liverpool.
Bradford have beaten Peterborough, Leyton Orient, Burnley and Rochdale to get to this stage.
Full quarter-final draw
Fleetwood Town v Everton/Newcastle
City v Bradford City
Crystal Palace v Sunderland
Liverpool v Bournemouth
