McGregor has been undergoing medical tests in
The 30-year-old has been looking for a new club after leaving Rangers when it was consigned to liquidation.
The Rangers newco, who McGregor declined to join, will dispute his right to move but the goalkeeper's former team-mates who followed the same route have been granted temporary transfer certificates by FIFA ahead of arbitration over possible compensation.
Like Rangers, Besiktas failed to meet financial criteria to gain a UEFA licence and could not take its place in this season's Europa League.
Turkish Super Lig
Kayserispor scored twice in the last 20 minutes to earn a 2-0 victory over third-placed Besiktas on the final day of the Super Lig season.