The 30-year-old has yet to play a game for the Catalan giants this season and currently sits behind Paulinho, Andre Gomes, Denis Suarez and mainstays Sergio Busquets, Ivan Rakitic and Andres Iniesta in the pecking order.
Turan has constantly struggled for regular action since arriving from Atletico Madrid in 2015 and his time at the Nou Camp finally appears to be up, with a January exit on the cards.
The playmaker now has to weigh up his options but will not be short of offers.
Galatasaray are keen to take him back to his homeland but reports in Spain claim that English Premier League side Arsenal are in the box seat to do a deal and have already been in touch with the player's agent.
Gunners boss Arsene Wenger wants a replacement for Mesut Ozil, who looks certain to be leaving the Emirates on a free transfer, and Turan could fit the bill perfectly.