A court has blocked assets including businessman Suleiman Kerimov's stakes in Uralkali and mining group Polyus Gold.
It was issued in response to a petition filed by Russian MP Ashot Egiazaryan in September.
Egiazaryan is embroiled in a business dispute over the landmark Moskva Hotel adjacent to the Kremlin, which has been undergoing redevelopment in recent years.
The action was mounted in Cyprus because it relates to companies registered on the island which hold stakes in Polyus and Uralkali.
After consultations with the court on Wednesday, lawyers for the sides said the mid-December session would hear whether the injunction should remain in force or be lifted.
The original injunction dated September 15 was issued without any of the respondents or their lawyers present.
The list of respondents includes Kerimov, former Moscow Mayor Yuri Luzhhov and his wife Elena Baturina.