The Black Eagles currently sit three points behind leaders Galatasaray in the Super Lig and plan to boost their title hopes with a big name signing in January.
L’Equipe understands that Besiktas are weighing up bid for Lyon forward Jimmy Briand.
Briand, 27, has missed last two months of action through a hamstring injury and he is likely to face an uphill task in an attempt to win back his place in the side.
Therefore, the France international might be willing to consider an offer from Turkey, with Besiktas expected to make a big money offer now that their highest earner Ricardo Quaresma has left the club.
While Lyon president Jean-Michel Aulas hope to keep hold of his prized asset, he may be prepared to sell him if the price is right.