The visitors head into the game on the back of a five-match winning streak, while the hosts are full of momentum after being victorious in the Dundee Derby on Saturday.
Match preview
Dundee United have not been able to win the Scottish League Cup since the 1980-81 campaign, and they are now presented with a great opportunity to progress to the semi-final on Thursday.
They will host Hibernian as they look to earn consecutive victories after being able to beat their local rivals at the weekend in the Scottish Premiership.
A goal from Ian Harkes in the 81st minute proved to be enough to secure three points in the Dundee derby which kept them fifth-placed in the table.
Even though their form has been mixed in the league, the Terrors have been dominant in this competition, having won all four of their group games with a trio of 1-0 results as well as an emphatic 6-1 victory against Elgin City.
Tam Courts then guided his team into the quarter-final by beating Ayr United, although it took an 80th-minute goal from the spot by Nicky Clark to keep them in it, eventually winning via a penalty shootout.
One problem that Dundee United have had this season is scoring goals, which is not something that Hibernian have had issues with as they have found the back of the net 12 in the league.
The visitors have been in brilliant form so far this season, which is why they are just one point behind Rangers in the Scottish Premiership, and are currently undefeated.
Even though they have actually won the same amount of games as Dundee United in the league, they are yet to be beaten outside of their failed Europa Conference League campaign.
Unlike their opponents, Hibernian did not enter the tournament until the second round, meaning they have only played once in the Scottish League Cup so far, which saw them knockout Kilmarnock with a 2-0 win.
That result kickstarted a five-game unbeaten streak which the team are currently on, although three of those matches were draws, including their two most recent outings against Hearts and St Mirren.
Hibs conceded in the 88th minute on Saturday to let their lead slip, despite goals from Paul McGinn and Martin Boyle originally bringing them back from behind.
Jack Ross does have a history of being able to knock Dundee United out of cup football though, as Hibernian actually defeated the Terrors 2-0 in the Scottish FA Cup last season in the semi-final.
Dundee United Scottish League Cup form:
Dundee United form (all competitions):
Hibernian Scottish League Cup form:
Hibernian form (all competitions):
Team News
Ilmari Niskanen has started the last two games for Dundee United after joining the club, while Callum Butcher has also featured in the heart of midfield after returning from injury.
Ryan Edwards was forced to come off during the game with St Mirren due to a problem, however, he was able to start during the Dundee derby, providing more experience to the defensive side of the team.
The Terrors were also able to welcome back Benjamin Siegrist in goal, with the number one shot-stopper making his return to the starting XI, but Courts will be without Liam Smith, who is currently injured.
For Hibernian, they could be without James Scott who had to miss out on their previous game due to illness, but there is a chance he could overcome that in order to be available.
Jamie Murphy is another player on the injured list for Hibs, as the winger continues to deal with a hamstring issue, while Sean Mackie and Christian Doidge are also out of action at the moment.
Dundee United possible starting lineup:
Siegrist; Smith, Edwards, Mulgrew, McMann; Niskanen, Butcher, Harkes, Fuchs, Pawlett; McNulty
Hibernian possible starting lineup:
Macey; McGinn, Porteous, Hanlon; Cadden, Magennis, Doyle-Hayes, Doig, Newell; Nisbet, Boyle
We say: Dundee United 1-2 Hibernian
This should be a closely contested game of cup football, with both teams being in reasonable form at the moment, but Hibernian should have enough quality to see them through.
This is mainly down to the attacking capabilities of the squad, with the visitors having proven themselves to be ruthless in front of goal, which is crucial in a competition such as this.