Danny Wilson's side have won four of their six homes this season and beat the impressive League Two side Rotherham 2-1 in the previous round.
The Bantams boast an alarming away record in League Two with no wins from seven but they impressively knocked out Huddersfield on penalties at the Galpharm Stadium in the round-of-16, and will have no fear as they prepare for the Blades.
The winner of the re-arranged tie between Accrington and Tranmere will face Chesterfield in the quarter-finals.
The teams will play again on Wednesday after their clash was abandoned following a serious injury to Tom Bender while the Spireites overcame Notts County 3-1 at Meadow Lane.
Full Area Quarter-Final Draw:
Rochdale vs Preston North End
Chesterfield vs Accrington Stanley or Tranmere Rovers
Sheffield United vs Bradford City
Oldham Athletic vs Crewe Alexandra
Swindon Town vs AFC Wimbledon
Cheltenham Town vs Barnet
Oxford United vs Southend United
Brentford vs AFC Bournemouth
Ties to be played the week of 7th November.