Both teams have amassed five points from their opening five games so far, and while the hosts are currently ahead on goal difference, Galatasaray's fate is also in their own hands.
Match preview
Taking a praiseworthy four points from two November fixtures against Manchester United and Bayern Munich has Copenhagen currently in the driving seat for a second-placed finish in Group A, having followed up an enthralling 4-3 beating of Man United with a much more low-key 0-0 with the German title holders.
With Bayern already confirmed to have won the group, Copenhagen benefitted from Thomas Tuchel's experimentation to hold out for a precious point, one which leaves them in second place in the section courtesy of their mildly superior goal difference to upcoming foes Galatasaray.
However, that stalemate with Bayern came in the middle of a disappointing five-game winless run for Jacob Neestrup's side, who have hit a Superliga plateau with a draw and two defeats from their last three games, and their Danish Cup journey was also brought to a premature end over the weekend.
Despite snapping their winless streak with a 2-1 win away to Silkeborg, a 2-0 home beating in the first leg dumped the capital giants out in the quarter-final stage, and Tuesday's European encounter presents Copenhagen with one last opportunity to end 2023 on a high.
While victory would ensure a ball in the last-16 pot for Copenhagen, whose only previous knockout appearance in Europe's premier tournament came in the 2010-11 campaign, a draw would also suffice if fourth-placed Man United fail to get the better of Bayern, but neither the hosts nor the visitors will leave anything to chance on Tuesday.
Not the first team to benefit from a couple of Andre Onana howlers this season, Galatasaray are also in control of their continental destiny thanks to a stellar turnaround against Man United last month, coming from 3-1 down to hold Erik ten Hag's team to a 3-3 stalemate.
While Onana could be partially forgiven for letting in Hakim Ziyech's first swerving free kick, the Moroccan had no right to beat the Cameroonian with his second set piece, which preceded a Kerem Akturkoglu piledriver in a six-goal extravaganza.
Okan Buruk's men embark on their Scandinavian sojourn with a superior attacking record to Copenhagen - scoring 10 times compared to the hosts' seven - but with the Danish side only shipping eight goals, a Galatasaray team who have been breached 12 times occupy the Europa League berth heading into Tuesday's winner-takes-all contest.
Domestic form has eluded Copenhagen recently, but Galatasaray have warmed up for the midweek clash in ideal fashion, extending their winning run in the Turkish Super Lig to three matches with a 2-0 success over Pendikspor and 3-1 success over Adana Demirspor on Friday evening.
As was the case in their thriller with Man United, Galatasaray harnessed their comeback powers against Copenhagen in September - coming from two goals down to hold the Danish champions to a 2-2 draw - but their only previous meeting in Scandinavia 10 years ago ended in a 1-0 win for the hosts, a positive omen for the more superstitious supporters.
Copenhagen Champions League form:
D
D
L
L
W
D
Copenhagen form (all competitions):
W
W
D
L
D
L
Galatasaray Champions League form:
W
D
W
L
L
D
Galatasaray form (all competitions):
L
L
W
D
W
W
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Team News
A quintet of Copenhagen players will likely remain confined to the infirmary for Tuesday's game, including defensive duo Birger Meling and David Khocholava, both of whom are targeting returns in January from muscle and knee injuries respectively.
William Clem is following a similar timeline as he recuperates from a devastating broken leg, while there is no indication when Noah Sahsah (knee) and Khouma Babacar (unspecified) might return, but the pair would have only made the bench on Tuesday anyway.
A couple of attacking alterations should be on the cards for Neestrup, who gave Andreas Cornelius the nod for the weekend's beating of Silkeborg, but Viktor Claesson is now primed to return in between Mohamed Elyounoussi and the much-coveted Roony Bardghji.
Since scoring a brace against Man United on the penultimate matchday, Galatasaray winger Ziyech has come down with a minor injury, which prevented the on-loan Chelsea man from contributing to the win over Adana Demirspor.
However, Ziyech's omission from the squad on Friday was believed to have only been a precautionary measure given what is at stake on Tuesday, so the Morocco international could very well be brought straight back into the fray over Tete.
Besides Ziyech, Galatasaray's only other fitness concern comes in the shape of Davinson Sanchez, whose hamstring strain is not expected to heal in time for the trip to Denmark.
Copenhagen possible starting lineup:
Grabara; Jelert, Vavro, Boilesen, Diks; Lerager, Falk, Goncalves; Bardghji, Claesson, Elyounoussi
Galatasaray possible starting lineup:
Muslera; Boey, Nelsson, Bardakci, Angelino; Ndombele, Torreira; Ziyech, Mertens, Akturkoglu; Icardi
We say: Copenhagen 2-3 Galatasaray
The footballing gods should bless the Parken Stadium turf with goals on Tuesday evening, as only a win will do for both sides if they are to make 100% certain of a knockout appearance, and attacking proficiency is where Galatasaray's strengths lie.