The Dutch outfit are keen to buy a new right back following Jan Kromkamp's sale to Spanish side Villarreal.
AZ have turned their attention to Khizanishvili after failed moves for PSV's Michael Lamey and Utrecht's Tim Cornelisse.
The Georgian defender is currently out of favour at Ibrox.
Former Rangers striker Shota Arveladze, who joined AZ from Rangers this summer, has recomended his new club to move for his fellow countryman.
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