The Judicial Service Commission has invited written submissions to help it decide if the complaint by Constitutional Court judges against Cape Judge President John Hlophe should be held in public.
Acting chairman Judge Craig Howie said the commission wants the parties to decide if the hearing should be open to the public and whether the media should cover it.
Written submissions must reach the commission by 3pm next Tuesday, he said.
The top judges complained after Hlophe allegedly tried to influence two fellow judges, Bess Nkabinde and Chris Jafta, to ensure the court ruled in favour of ANC president Jacob Zuma against the Scorpions.
Hlophe allegedly told the two judges that he was acting on a mandate, had connections with intelligence services and politicians, and that Zuma was being persecuted.
Experts said Hlophe faced impeachment if found guilty.