The Dutch left-back's existing deal expires at the end of the season and as yet no agreement on a new deal has been reached.
The Gala proposal is understood to be a three year contract with a sharp increase on his reported £55,000-per-week deal with Palace, says the Daily Mail.
Likewise, a move to Istanbul would likely see Van Aanholt have the opportunity to play Champions League football next season with Gala currently occupying second place in the Turkish Super Lig - three points adrift of leader Besiktas.
Van Aanholt turns 31 in August meaning this deal will likely be his last major pay day.
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