The Derby midfielder, who has been told he is surplus to requirements at Pride Park, is holding out for better offers before deciding his future.
Galatasaray have been tracking the skilful midfielder for some time and have been in talks for the past month about a move to The Ali Sami Yen.
Despite turning down Gala's offer, the player is still destined to leave Derby for pastures new.
"Galatasaray are a great club but I expect better offers," said Kinkladze.
The 33-year-old playmaker has been allowed to return home to Georgia to sort out his future and will miss the final game of the season next week away to Sunderland.
Rams boss John Gregory is determined to offload a number of players after suffering relegation to Division One as he looks to cut the side's wage bill.
