The Turkish TV channel Kanal A claim that the transfer could signal an exit for the Turkish international this summer.
Ben Arfa would be direct competition for Turan if Barcelona decide to sign him. However, Turan recently reaffirmed his desire to remain at Barcelona despite enduring a difficult start at the Catalan giants.
Turan has gone onto make just nine starts for the Catalan giant and has been linked with moves away from the club.
“To wear this jersey alongside the likes of Iniesta, Messi, Suarez and Neymar is amazing,” Turan was quoted as saying by the Hurriyet.
“I will not give this up easily, I am willing to remain patient.”
Barcelona take on Grana in the final day of the La Liga season this weekend.