The Rovers are the only team from the Scottish Championship remaining in the competition, while the Hoops last won the trophy during the 2019-20 season.
Match preview
Celtic had to go through a difficult test in order to book their place in the quarter-finals, with a five-goal thriller against Hearts in the second round.
Goals from Odsonne Edouard, Stephen Welsh, and Kyogo Furuhashi helped to secure the 3-2 victory to keep them in the competition which they have won 19 times in the past.
Last season the Hoops did not make it this far after being beaten by Ross County in the previous round, therefore there has already been an improvement, but they will now be aiming to be part of the final four.
Celtic have had a mixed start to the campaign in terms of form, with consistency proving to be an issue, which is why they currently sit sixth-placed in the Scottish Premiership with a trio of wins and losses to their name.
However, they have been serious attacking threats so far, scoring 16 goals in the league with a further 18 across other competitions, proving just how dangerous they can be.
Despite their goal threat, Ange Postecoglou's team were unable to find the back of the net on Saturday when they suffered their most recent defeat in a 1-0 loss against Livingston.
The result came as a surprise because the Lions had not won a game in the league until that point, and even though Celtic had 80% of the possession, they were unable to walk away with any points.
On the other hand, Raith Rovers head into this fixture in strong form having won four of their last five matches in all competitions, including a 1-0 victory against Greenock Morton on Saturday.
Dario Zanatta was on hand to score the only goal, which helped push his team to fifth place in the league as they continue to battle for promotion to Scotland's top flight.
In the Scottish League Cup, the Rovers have been impressive, topping their group without a defeat or conceding a goal, while they then went on to overcome another strong Scottish Premiership outfit in Aberdeen during the second round.
They had to fight back from behind to make it to the quarter-final, with a goal from Ethon Varian drawing them level before Zanatta found the back of the net to earn the win.
However, John McGlynn will have to hope his team have all the inspiration they need heading into the game, as Celtic have decided to not allow any away supporters into the stadium due to COVID-19 guidelines, making the challenge a little harder.
Celtic Scottish League Cup form:
Celtic form (all competitions):
Raith Rovers Scottish League Cup form:
Raith Rovers form (all competitions):
Team News
Celtic made four changes for the defeat against Livingston, with the team being hampered with injuries, and James McCarthy was one of those, as he started for the first time, while Liel Abada made his return as well.
Boli Bolingoli-Mbombo was able to appear from the first whistle, while Mikey Johnston was a used substitute as he came back from injury, which could see him in line for more minutes on Thursday night.
Welsh was also brought into the team, but he was not able to play for the full 90 minutes, as the defender was brought off later in the match.
However, the club will still be missing several important names, with Greg Taylor unavailable due to a shoulder problem, Furuhashi being out with a knee issue, and Callum McGregor also being on the shelf.
Zanatta will be sure to feature for the visitors at Celtic Park as he continues his fine form in front of goal this season, proving to be a true danger man for McGlynn's team.
However, the club are missing Lewis Vaughan for the entire season after he suffered a ruptured ACL, which has proven to be a big loss for the team.
Celtic possible starting lineup:
Hart; Juranovic, Carter-Vickers, Starfelt, Bolingoli-Mbombo; Rogic, Turnbull, McCarthy; Filipe, Abada, Ajeti
Raith Rovers possible starting lineup:
MacDonald; Dick, Berra, Benedictus, Tumilty; Riley-Snow, Tait, Matthews, Zanatta, Spencer; Varian
We say: Celtic 2-1 Raith Rovers
Celtic might be the firm favourites in this game purely down to their history and the fact they are in the higher league, but this will be no easy task for them.
However, with no away support to rally behind Raith Rovers, it will also be a tough challenge for the visitors, and in the end the quality of the Hoops should shine through.