The French defender has struggled to make an impact at the Turkish side.
The former France under-21 international joined the Turkish giants in the summer but has failed to establish himself at the club.
Therefore it is reported that Forest and Club Brugge are interested in snapping up the 24-year-old talent.
Carole, who left Troyes for Turkey, has also played for Nantes and Benfica in his eventful career and is a top talent.
Forest have something of an issue at left-back, with Dani Pinillos ruled out with a serious knee injury. Danny Fox is also expected to be sold.
However they recently picked up Bojan Jokic on loan from Villarreal and Chris Cohen has just returned to full action.
The deal is also said to be a cash offer, not a loan, which would seem to contradict the club's current regulations under their transfer embargo.
Carole would be a great signing, however it seems to carry little substance.