It is the first competitive meeting between the two sides since 2001, when they played out a 1-1 draw in the Premier League.
Match preview
Bradford have made a solid, if not spectacular start to their League Two campaign, having taken 13 points from their opening nine games, which leaves them in 11th place, two points off the playoffs.
There are signs that the Bantams are now starting to find their form, having gone on a six-game unbeaten run in all competitions, although they have drawn three of those, stumbling to a 1-1 draw against Harrogate Town in their last home match.
In a lot of games, Mark Hughes's side have looked better away from home, having defeated Accrington Stanley and Wrexham on their travels in the first two rounds of the EFL Cup to reach this stage of the competition.
The Bantams once again looked very promising on the road in their last match, defeating Newport County 4-1 at Rodney Parade after racing into a 3-0 lead inside half-an-hour, but they face a much more difficult task on Tuesday night.
Indeed, Middlesbrough are likely to pose far more of a challenge, given that they ply their trade two divisions higher than Bradford City, currently competing in the Championship, but they have failed to hit the heights expected of them so far this season.
Boro occupy a place in the relegation zone of the second tier, sitting in 22nd place, having only taken five points from their opening eight games, and they have been suspect defensively in a number of those matches.
Michael Carrick's side fell to a 3-0 defeat away at Coventry City back in August, before losing 4-2 at West Bromwich Albion in their following away match, and they have picked up just one point from their opening four Championship away games.
However, Middlesbrough managed to progress past Bolton Wanderers at the Toughsheet Community Stadium to reach this stage of the competition, chalking up a 3-1 win away at the League One side.
Not only that, but there was finally some respite for Boro in their last match, notching a 2-1 win at home against Southampton, with Riley McGree and Jonny Howson getting on the scoresheet, which should give them renewed confidence ahead of their upcoming games.
Bradford City EFL Cup form:
W
W
Bradford City form (all competitions):
W
W
D
D
D
W
Middlesbrough EFL Cup form:
W
W
Middlesbrough form (all competitions):
L
W
L
L
D
W
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Team News
Considering Bradford will need to be at their best to stand any chance of progressing, Hughes is unlikely to make too many changes to his side, but they were in action three days ago, and he could freshen up the starting lineup.
Emmanuel Osadebe could replace Clarke Oduor at right-wing, having featured as a substitute in the last match, while Taylor Smith may get the nod over Jamie Walker in attack, after scoring against Wrexham in the last round.
Middlesbrough are more likely to make a number of alterations, given that they are coming up against lower-league opposition, and Tom Glover could come in for Seny Dieng between the sticks, having started in the previous round.
There are no fresh injury concerns for Carrick to deal with, but Anfernee Dijksteel and Matt Clarke remain sidelined, having both been unable to feature so far this season.
Bradford City possible starting lineup:
Lewis; Halliday, Platt, Stubbs, Ridehalgh; Oduor, Gilliead, McDonald, Tulloch; Walker, Cook
Middlesbrough possible starting lineup:
Glover; McNair, Fry, Lenihan, Engel; Hackney, Barlaser, Crooks; Forss, Jones, Latte Lath
We say: Bradford City 0-2 Middlesbrough
Middlesbrough progressed past League One opposition away from home to reach this stage of the competition, and they should have no trouble beating a mid-table League Two side.
Having picked up a victory against Southampton in their last match, Carrick will be hoping his Boro side can now start to gather some momentum and kickstart their season.