Barkas has struggled to make an impact at Celtic Park since joining the club from AEK Athens and Bhoys boss Ange Postecoglou brought in a new number 1 in the shape of Joe Hart in the summer.
The Greek goalkeeper has little chance of playing at Celtic this season and he is poised to leave the club in January.
Barkas is attracting interest from several clubs in Turkey, though it remains to be seen which Super Lig sides want him.
He penned a four-year contract at Celtic when he joined the club.
The 27-year-old has made just one appearance for Celtic so far this season, turning out in a Champions League qualifier against Danish team FC Midtjylland.
He has been an unused substitute on numerous occasions and has made 23 appearances in total for Celtic since joining the club, keeping eleven clean sheets.
It is unclear how much Celtic want to let Barkas go and whether they will look to replace him if he does depart.