The Turkey international is expected to leave Barca next month and a return to Turkey has been mooted.
However, Orman says Besiktas won't be competing for his signature.
He explained: "Arda Turan is a player we appreciate, but he is not on our agenda.
"Arda is a player we love very much, he is important in Turkish sport. He is a player who represents us very well abroad but we cannot have him for Besiktas."