With Celtic already out, Rangers will see this as a fantastic opportunity to win this trophy for the first time since 2011.
Match preview
A change of fortunes is required, as Rangers have been extremely underwhelming in both domestic cup competitions since reforming in the fourth tier in 2012.
Despite having now been back in the top flight and competing for the title since 2016, Rangers have won just one domestic cup, the Scottish Cup in 2022, while being losing finalists on three occasions.
Hearts were the side they beat to claim that one piece of silverware in 2022 though and the Rangers faithful will hope that is a good omen for them heading into this semi-final.
Spirits are also much higher at Ibrox since Michael Beale's sacking, as Rangers have won four from four domestically since his dismissal.
Hearts were one of the sides they have beaten in that time, and new manager Philippe Clement oversaw that victory, as well as thrashings over Hibernian and Dundee.
It might already be too much to overturn though, as a five-point deficit to Celtic looks insurmountable given how dominant their Glasgow rivals usually are.
While still being in contention to progress through the Europa League group stages, Rangers' best bet for silverware may come in the three cup competitions this season, making this undoubtedly Clement's biggest match since taking over.
Tynecastle has been a pleasant place to visit for the Rangers support in recent times too, as they have won four in a row here by an aggregate score of 12-1.
Hearts have beaten Rangers just three times since the Glasgow giants returned to the top flight in 2016, but they all came here at Tynecastle.
The most memorable was the 2020 Scottish Cup quarter-final win which saw Liam Boyce net a late winner in a 2-1 victory.
Darker memories such as the 2022 Scottish Cup final defeat to Rangers have been more common for Hearts though, as that was their third final loss in the last four years, so their support will be desperate to see them go one better this season.
The League Cup has not been as successful for the Edinburgh club, as this is just their third semi-final in 10 seasons.
Manager Steven Naismith will be glad his side are coming into the game on the back of a win though, as they dominated Livingston in midweek despite only having only one goal to show for it.
It was a much-needed three points as it moved Hearts back up to fourth, after defeats to Celtic and Rangers saw them slip down the table slightly.
Hearts Scottish League Cup form:
W
W
Hearts form (all competitions):
W
W
D
L
L
W
Rangers Scottish League Cup form:
W
W
Rangers form (all competitions):
L
W
W
D
W
W
Advert - content below:
Team News
Hearts will be without Australian right-back Nathaniel Atkinson, as an ankle injury is set to keep him out for another month at least.
Knee problems currently have Barrie McKay and Craig Halkett sidelined, but returns for both players are believed to be close.
After being the match winner in that 2020 Scottish Cup quarter-final, Boyce may have to fight for his place ahead of Costa Rican Kenneth Vargas, who scored the winner in midweek.
Clement should go full strength with his Rangers side here despite having a big European tie with Sparta Prague at Ibrox on Thursday.
On the injury front, Rabbi Matondo and Kemar Roofe are both set to miss out in attacking areas, but should make comebacks before the end of the month.
Tom Lawrence is also currently out for the visitors with a calf injury, so Scott Wright will hope he can keep his place out wide, while after scoring in back-to-back games, Danilo may get the nod up front ahead of Cyriel Dessers.
Hearts possible starting lineup:
Clark; Sibbick, Kent, Rowles; Offiah, Nieuwenhof, Baningime, Grant, Cochrane; Shankland, Vargas
Rangers possible starting lineup:
Butland; Tavernier, Goldson, Souttar, Yilmaz; Lundstram, Jack; Wright, Lammers, Sima, Danilo
We say: Hearts 1-2 Rangers
In what is set to be a hard-fought, intense semi-final between two sides desperate to add silverware, Rangers may just have the firepower to claim a place in the final.