Melo recently returned to individual training after recovering from his hernia operation.
The Brazilian midfielder has started being introduced to team training sessions however, Melo still faces a race against time to fully recover in time for the Trabzonspor game.
Galatasaray have struggled in the past when the Melo has been suspended or injured.
Melo missed four games in the 2013-2014 season due to suspension and the Istanbul giants failed to win any of those game.
However, the Lions have managed to cope better without the Brazilian midfielder this time around.
Galatasaray have won four, drawn one and lost one league game without Melo.
The 30-year-old joined the Istanbul giants on a permanent deal from Juventus worth £3 million last summer after playing the previous two seasons on loan at the Lions.