The Moroccan joined Malaga on loan in January 2014 in an attempt to revive his career and he has largely impressed at La Rosaleda.
Amrabat immediately nailed down a regular starting berth and went on to score two goals and produce five assists in 13 La Liga outings.
As a result, Malaga officials have twice travelled to Istanbul to try and reach an agreement over a permanent transfer, but their efforts have so far proved unsuccessful.
Greek giants Olympiakos have submitted an official proposal for the 27-year-old footballer, while Valencia, Sevilla and Levante are keeping close tabs on the player as well.
Having all but secured La Liga survival, Malaga travel to Vicente Calderon next weekend to face league leaders Atletico Madrid and they are priced at 7/2 to avoid defeat to los Colchoneros.