Wrexham beat Wigan Athletic on penalties to secure their place in the second round, while the Bantams prevailed in their shootout with Accrington Stanley.
Match preview
Having returned to the Football League after a 15-year absence, Wrexham have experienced a mixed start to the season, picking up six points from their opening five league matches.
After playing out an entertaining 5-5 draw with Swindon Town, Phil Parkinson's side had to settle for another point in Saturday's away meeting with Barrow.
Elliot Lee dispatched his 12th-minute spot-kick to take a slender lead into half time, but Barrow managed to find an equaliser in the second period, ensuring Wrexham had to settle for a third draw in four league games.
While a flurry of draws may frustrate Parkinson, his side are currently unbeaten in five competitive matches, and they will be determined to keep that run going when they face Bradford for the first time since 2008.
After eliminating Wigan in the previous round, the Red Dragons are hoping to reach the third round of the EFL Cup for the first time since the 1981-1982 season.
Meanwhile, Bradford have experienced a mixed start to the 2023-24 campaign, which began with a narrow 1-0 defeat to Crawley Town.
The Bantams bounced back to beat Accrington on penalties in the EFL Cup, before they picked up four points from their next two league games.
Although they were stopped in their tracks by a disappointing 3-0 defeat to Morecambe, Bradford responded in impeccable fashion to edge out Crewe Alexandra on Saturday courtesy of Jamie Walker's first-half effort.
Mark Hughes would have been pleased to see his side record their first clean sheet of the season, and he will now be challenging his side to produce another strong defensive display on Tuesday.
The visitors, who reached the final of the EFL Cup in 2013, are hoping to reach the third round of the competition for the first time since the 2014-15 season.
Wrexham EFL Cup form:
W
Wrexham form (all competitions):
L
W
D
W
D
D
Bradford City EFL Cup form:
W
Bradford City form (all competitions):
L
W
W
D
L
W
Advert - content below:
Team News
Paul Mullin is still unavailable as he continues to recover from four broken ribs and a punctured lung sustained during a pre-season friendly with Manchester United.
Mark Howard was brought into the side to replace Ben Foster on Saturday after the former Watford goalkeeper retired from football following the club's 5-5 draw with Swindon, and the 36-year-old is expected to retain his place between the posts for Tuesday's contest.
After dropping down to the bench for Saturday's away meeting with Barrow, James Jones could be recalled to the starting lineup for the midweek cup tie.
As for the visitors, Walker is expected to retain his place in the side after marking his return from injury with a goal
Richard Smallwood lost his place for Saturday's league win, but the Bradford captain is in contention to start against Wrexham.
Andy Cook will be looking to open his goalscoring account for the season when he leads the line in Tuesday's cup tie.
Wrexham possible starting lineup:
Howard; Forde, O'Connell, Tozer, Boyle, Mendy; O'Connor, Young, Lee; Bickerstaff, Palmer
Bradford City possible starting lineup:
Lewis; Platt, Stubbs, Kelly; Oyegoke, Pattison, Smallwood, Richard; Smith, Walker; Cook