Coyle is resigned to losing the Sweden international, who has scored 12 goals in all competitions this season after just 10 in the past two campaigns.
"Galatasaray have announced on their website they have agreed something with Johan," Coyle said.
"I have spoken to Johan and certainly nothing has been signed. That is not to say it won't be signed, maybe in the next couple of weeks but not before Sunday.
"Do I expect him to leave? In my heart of hearts, yes. These are the things you have to deal with as a manager. I am very comfortable with that.
"I have always felt and always known given the dialogue (chairman) Phil Gartside had with his representative they were probably looking for a new option.
"I personally wish Johan well if and when that comes about because he has worked ever so hard for me in training each and every day.
"When he has worn that shirt he has given me everything he has got in a number of positions and worked his socks off for the team. He is someone I have a very good relationship with."