Arveladze reportedly offered the striker, 26, a £4million deal over two years to join the Turkish club.
However, former Ibrox player Arveladze was left frustrated when the Scottish Premier League's record goalscorer, also linked with a move to Middlesbrough and Blackburn, turned down the invitation to fly to Turkey for discussions.
"It is 95% certain now that Kris won't be coming and, of course, I am disappointed because I wanted him in my team," Arveladze told the Scottish Daily Mail.
"He didn't even want to come out here and see the place. I don't know why. I don't know if it is because he wants to stay in Britain or if there's now a chance he'll remain at Rangers.
"I've lived all over Europe and this is a lovely place. I made him my best offer and spoke personally to Kris a couple of times. I also met his agent, Mark Donaghy. But Mark has now told me it won't happen and I am just waiting for formal rejection of our offer."