There are 38 games right? If I am not wrong that means there is 15 more games left, 45 possible points. Even if they could get like 30 of those, that is going to be midtable at the very worst case for them. It means around 2 points for each 3 point possibility, a lot of wins, a bit of draws and very few losses. Could they do that? They potentially could, if it was all about the roster then they wouldn't be able to go to next stage in europa, they are decent enough to go to next stage so they are capable of doing better in the league.
I don't think that Galatasaray will be able to achieve the mid-table position in this season. Yes, there are still 15 matches left but I think they are going to lose a lot of them. At least they haven't proven anything to you make me believe they are going to improve in this season. In my opinion, they will just be able to survive the last 4 spots.
The key word here is "capable", just because they are capable doesn't mean they will be able to do it. Just realize that they are not really doing something that they should be doing right now, and that shows that they suck at the league so they could also keep doing bad in the league as well. They may not relegate, but they do not feel like they will recover too much neither.
But the positive thing is the points difference is not really very big so they can go up really quickly if there win two or three games consistently. But, I don't think they will be able to perform consistently and the best scenario is that they might get 3-4 wins in the 15 matches left.