The resignations, which have not been officially confirmed, come amid opposition claims that President Mikheil Saakashvili is trying to exert control over the Supreme Court.
At the core of the dispute are amendments brought a few months ago to the law on the Supreme Court. The changes say judges who quit by the end of this year will receive pensions equal to their salaries.
Critics claim the government is considering using the new regulation to rid itself of magistrates it deems not loyal enough.
Georgia's Higher Council of Justice is currently examining the case of three Supreme Court judges accused of allegedly delaying court cases. The council can either give the magistrates just a warning, or refer the matter to Saakashvili.