Among seven people arrested on Tuesday in connection with the murder, one was identified as the man who stabbed 25-year-old Marko Ivkovic.
Arrests came after the police studied footage recorded by security cameras in the area.
Ivkovic was stabbed in the chest when crowd trouble turned violent after Red Star fans allegedly arrived at the venue without tickets for the game, according to the Istanbul police department.
The violence began with rival team fans throwing stones and bottles at each other, the statement added.
Serbia summoned the Turkish ambassador to Belgrade earlier this week after relations between the two countries were rocked by the crime.
"We deeply regret the loss of Serbia citizen Marko Ivkovic's life. Serbia-Turkey relations have too strong basics to be affected by such an incident," Turkey's foreign ministry spokesman told reporters on Thursday.
A water polo match between Galatasaray and Partizan in Serbia to be played on Saturday was postponed to a later date.
Turkish media reported that Istanbul police would escalate security measures before Galatasaray face Olympiakos on Dec. 19, as Greek and Serbian fans have vowed revenge on online forums.
(Additional reporting by Tulay Karadeniz in Ankara, Writing by Ece Toksabay; editing by Justin Palmer)
