Scotland goalkeeper Allan McGregor is in talks with Besiktas, according to the Turkish club's official website.
McGregor is one of 11 players who refused to move to the Rangers newco, although the club contests their right to move as free agents.
The Scottish FA has refused to grant international transfer clearance to five players who have found new clubs.
Besiktas, from the European side of Istanbul, finished fourth in the Turkish Super Lig last season.
However, the Black Eagles have been banned from European competition for one season due to financial problems.
Rangers have been McGregor's only permanent club, although he had spells on loan at St Johnstone in 2004-05 and Dunfermline the following season.
The 30-year-old Edinburgh-born goalkeeper has been capped 21 times for Scotland.