According to reports in the French media, Forest are keen to land the 32-year-old Senegalese midfielder to their growing ranks even further, and could beat several Turkish clubs to his signature.
Kouyate left Palace after failing to agree a new contract with the Selhurst Park club, as he looks to collect one big final pay day with his career drawing to an end.
Nottingham Forest have been on the hunt for some added steel in their midfield, having missed out on Paris Saint-Germain midfielder Idrissa Gueye who is on the verge of a return to Everton.
The experienced Kouyate certainly fits the bill. Forest manager Steve Cooper admitted before the opening day away defeat to Newcastle on Saturday that the club were still searching for new faces to add to the 12 he had already brought in.