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 side Fenerbahce could face another ban from the UEFA Champions League after UEFA announced the club and five officials will have match-fixing charges heard by its disciplinary body later this month.