The playmaker has been frozen out of the first team by Alan Pardew and has been recommended to the Turkish club by former Magpies teammate Demba Ba.
The French playmaker has not started a competitive game for the club since being replaced at halftime in the 4-0 defeat to Southampton on March 29 and has been frozen out of the first team squad this season by Alan Pardew.
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The 27-year-old was a firm fan favourite after moving to St James' Park from Marseille in 2010 but Pardew has decided that the playmaker is now surplus to requirements.
Ben Arfa has rebuffed interest from clubs in the Middle East this summer and Turkish club Besiktas has now opened talks to take the forward to Istanbul.
The Frenchman's former Newcastle teammate, Demba Ba, who left Chelsea for Besiktas this summer, is understood to have recommended him to coach Slaven Bilic.
Besiktas is now hopeful that the club can complete a deal to sign Ben Arfa as it looks to mount a title challenge this season following its elimination from the Champions League at the hands of Arsenal.