The Gunners were linked with the French international over the summer, but saw their pursuit of his signature thwarted by the La Liga side’s desire to keep him at the Bernabeu.
However, Real are rumoured to be willing to sell this winter as they look to fund a move for Liverpool striker Luis Suarez.
Arsenal are believed to remain interested in the ex-Lyon man, and have been linked with a serious offer for his services once the transfer window re-opens.
But, Gala are now keen with new boss Roberto Mancini already lining up targets to bolster his inherited squad.
The former Manchester City coach recently took control of the Turkish giants and is ready to draft in players that closely suit his preferred playing style.
Benzema is thought to be one of his top targets, thanks to his razor-sharp edge in front of goal.
Gala could free up space for the 25-year-old by allowing Chelsea target Burak Yilmaz to leave the club.
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