The struggling Super Lig champion will be out to kick start its European campaign after picking up its first win in eight games at the weekend.
Galatasaray will hope to put its poor start to the season behind it when the club hosts Copenhagen in Istanbul on Wednesday.
The Super Lig champion won its first match in eight on Saturday, with Wesley Sneijder's double giving the team a badly needed 2-1 home win over a 10-man Karabukspor.
The result lifted the team to 10th in the table, and new manager Roberto Mancini is sure to demand more from his squad as the season goes on, starting with the Group B Champions League encounter against the Danes.
Sneijder has scored just seven goals since moving from Inter in January, and president Unal Aysal said it was about time the Dutchman started performing.
"Sneijder produced the type of performance [against Karabukspor] that we expected from him for the first time," Aysal said.
"Naturally, we have high expectations of him. We have waited for this for months."
The match - which will be Galatasaray's 250th in UEFA competition - will give the club a chance to respond to a dreadful performance against Real Madrid in its last home outing in the Champions League.
Galatasaray was embarrassed as Cristiano Ronaldo scored a hat trick in Real Madrid's 6-1 victory in Istanbul.
The team improved in its second fixture, with Umut Bulut's 88th-minute equalizer giving the team a point in a 2-2 draw at Juventus.
Copenhagen have recovered from a poor start of their own, winning three of their last four matches in the Danish Superliga.
That has seen it climb to sixth in the table, although a 3-0 home triumph against Aalborg on Sunday saw the club keep its first clean sheet in 18 matches.
Copenhagen only qualified the group stages of the Champions League after Galatasaray's rival, Besiktas, was kicked out for its involvement in a match fixing scandal.
Stale Solbakken's side lost its playoff to Lille - 2-1 on aggregate - but was placed in Group B after Besiktas was punished.
The last time the team was involved in the group stages of the Champions League, Copenhagen reached the round of 16 against the odds.
A similar performance is unlikely this time around, but a surprise win at the out-of-form Galatasaray would boost its chances.
The club made a bright start to its Champions League campaign, claiming a surprise 1-1 home draw against Juventus, but was beaten 4-0 at Real Madrid in its last fixture.
MasterCard is excited to present episode one of the Priceless Memories UEFA Champions League video series. See what Liverpool legend Didi Hamann has to say about the infamous 2005 final!