The veteran defender is seeking a release from the final year of his Atleti contract.
And AS says that there is great interest from Turkey.
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Fenerbahce, Besiktas and Trabzonspor are all said to be after the 33-year-old.
The three clubs are said to have all made contact with the centre-back's agent Zarko Pelicic.
Pelicic will now ask Atletico Madrid to release Savic from the final 12 months of his current contract.