The hosts defeated St Johnstone to progress to this stage, while the visitors humiliated Airdrieonians 6-1 in their second-round tie to advance to the quarter-finals.
Match preview
Rangers have endured an extremely inconsistent start to 2024-25, a campaign in which they had pre-season ambitions of ending Celtic's dominance since their last Scottish Premiership title in 2020-21.
In the three seasons since, Rangers have won just two trophies, claiming the Scottish Cup in 2021-22 and the Scottish League Cup last year, while their bitter rivals, Celtic, have secured three consecutive league titles, two Scottish Cups, and two Scottish League Cups.
Unfortunately for Philippe Clement, his side's inconsistent start to the season already has them trailing Celtic by five points in the league, and they have also been knocked out of the Champions League following a 3-1 aggregate defeat to Dynamo Kyiv in the third qualifying round.
With three wins in their last four matches, despite a 3-0 loss to Celtic, Clement's side seem to be turning a corner as he now shifts his focus to attempting to retain Rangers' Scottish League Cup trophy.
They will face stern competition in their quarter-final tie though, with Dundee enjoying a brilliant start to the season that has seen them lose just one of their first 10 matches.
Tony Docherty's men kicked off the term by going undefeated in their first nine matches, continuing the impressive form that saw them finish sixth in their return to the Scottish Premiership last season.
Their sole defeat of the campaign came in their last outing, a 2-0 loss to Ross County, with Docherty now aiming to bounce back with a win in Saturday's quarter-final.
Dundee have struggled in this fixture over the years, with their last victory against Rangers coming in November 2017, leaving them 13 meetings without a win, 11 of which ended in defeat.
Rangers Scottish League Cup form:
W
Rangers form (all competitions):
W
L
W
W
L
W
Dundee Scottish League Cup form:
W
W
W
W
W
Dundee form (all competitions):
D
W
W
D
D
L
Team News
The hosts will be without Danilo, who is out until October with a knee injury, Rabbi Matondo, who is out until December with a hamstring injury, and Ridvan Yilmaz, who is out until later this month with a thigh injury, for this match.
Elsewhere, they may revert to the lineup that secured a 2-0 victory over St Johnstone in the Scottish League Cup second round, with the only changes seeing Cyriel Dessers and Oscar Cortes replace the injured Danilo and Matondo.
The visitors could be without the services of Charlie Reilly, who remains a doubt due to a hamstring injury that has kept him out of the side since July.
Defenders Clark Robertson and Joe Shaughnessy are both also unavailable due to injury issues, meaning Juan Portales and Billy Koumetio are likely to continue in central defence.
Rangers possible starting lineup:
Butland; Tavernier, Propper, Souttar, Sterling; Diomande, Jefte; Cerny, Dowell, Cortes; Dessers
Dundee possible starting lineup:
McCracken; Ingram, Portales, Koumetio, Larkeche; Mulligan, Sylla, Cameron; Palmer-Houlden, Murray, Tiffoney