The former lawyer is suing the State of Victoria for damages, claiming officers put her safety at risk and her unmasking as a police informer damaged her health and career.
The case has been set down for a Supreme Court trial later in September, with Ms Gobbo expected to attend in person.
Her barrister Tim Tobin SC on Wednesday flagged his client would make an application to recuse the state's judges from presiding over the trial.
He said Ms Gobbo had concerns with the Victorian judiciary, particularly former director of public prosecutions Kerri Judd, who decided against charging those implicated in the Lawyer X saga and was made a Supreme Court justice on Tuesday.
"I'm instructed to say the plaintiff is so concerned she would seek someone other than a member of the court," he told the court on Wednesday.
The application was due to be heard in the Supreme Court on Thursday afternoon, but the court confirmed the hearing was vacated as the application was no longer being pursued.
Justice Andrew Keogh will still need to determine whether the trial is determined by jury or a judge alone.
The state is pushing for a judge-alone trial, noting a jury could be tainted by the extensive publicity surrounding Ms Gobbo.
The case was also legally and factually complex, which could be problematic for a jury, state barrister Bernard Quinn KC told the court on Wednesday.
Ms Gobbo is seeking a jury trial, with Mr Tobin stating she believed other citizens could more objectively determine her case.
Justice Keogh will hand down his decision on the jury application at a later date.
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