The Danish outfit came out on top by a 2-1 scoreline last week, and they will fancy their chances of avoiding defeat given the recent form of their opponents.
Match preview
Given their dominance of the Super Lig in 2021-22, Trabzonspor will feel that they deserve their first experience of the Champions League group stages since 2011-12.
However, Abdullah Avci's side will have to shake off two disappointing defeats in succession to earn their place at European football's top table.
The only positive from the first leg in Denmark was Anastasios Bakasetas's goal 11 minutes from time after Copenhagen had established a two-goal lead by the 48th minute.
Trabzonspor then went on to ship five goals away at Antalyaspor at the weekend, succumbing to a 5-2 loss with three of the home team's goals coming from the 80th minute onwards.
The level of capitulation will worry Avci with his team having gone from keeping three clean sheets in a row to conceding seven times in two matches.
At a time when Trabzonspor sit in eighth position in Turkey's top flight, Copenhagen are down in fifth spot in the Danish equivalent after a mixed start on the domestic scene.
Jess Thorup has witnessed the defending champions lose three of their opening six matches with each win being followed by a defeat, although they now have two successive victories in all competitions.
On the back of the success in the first leg, the Lions made light work of Lyngby, cruising to a 3-0 triumph on away territory with all three goals coming inside the opening 52 minutes.
Viktor Claesson and Pep Biel have netted five strikes apiece on the domestic scene and offer the biggest threat for the away side.
Trabzonspor Champions League form:
Trabzonspor form (all competitions):
Copenhagen Champions League form:
Copenhagen form (all competitions):
Team News
Having made numerous changes to his side at the weekend, Thorup could revert back to the team which started the first leg.
That is more likely with Thorup having been able to rest players during the second half against Lyngby, while Kevin Diks should return at right-back despite the knock that he sustained last week.
There is more uncertainty around the Trabzonspor XI with Avci having made two changes before half time versus Antalyaspor given the performance of his side.
Enis Bardhi scored twice as a substitute and should earn a chance in a creative role, with Marc Bartra an option in the centre of defence.
Stefano Denswil's place may be at risk having been replaced in the last two games, but Vitor Hugo was withdrawn at the break on Saturday.
Trabzonspor possible starting lineup:
Cakir; Stryger Larsen, Hugo, Bartra, Elmali; Bardhi, Siopis, Bakasetas; Kouassi, Cornelius, Trezeguet
Copenhagen possible starting lineup:
Ryan; Diks, Vavro, Khocholava, Kristiansen; Falk, Zeca, Lerager; Haraldsson, Biel, Claesson
We say: Trabzonspor 1-1 Copenhagen (Copenhagen to win 3-2 on aggregate)
Trabzonspor's bigger issues come in defence and much of their focus may be on keeping things tight at the back over initially pushing to win this contest. That mentality may allow Copenhagen to gain a foothold in the game, leading us to predict a low-scoring draw which will suit the visitors.