In a brief Federal Court hearing on Thursday, Justice Michael Wigney asked if a second round of negotiations would be fruitful after December talks broke down between Mr Murdoch and Private Media, the publishers of Crikey.
"I suppose a further mediation is out of the question," the judge said.
"I think the parties understand each other's positions," Crikey's barrister Michael Hodge KC replied.
Murdoch's barrister Sue Chrysanthou SC did not take up the judge's offer either.
The son of Rupert Murdoch has sued Private Media over an allegedly defamatory June 29 opinion piece that was taken down and then posted back online on August 15 in what he claims was a "dishonest" campaign enticing him to sue the publisher.
Lachlan Murdoch alleges the article titled "Trump is a confirmed unhinged traitor. And Murdoch is his unindicted co-conspirator" conveyed a meaning that he illegally conspired with former president Donald Trump to "incite a mob with murderous intent to march on the Capitol" in Washington DC on January 6, 2021.
The case was originally also filed against Crikey political editor Bernard Keane and editor-in-chief Peter Fray.
On Monday, the media mogul was allowed to draw Private Media chairman Eric Beecher and CEO Will Hayward into the case.
The amendments meant the trial, which was scheduled to begin in March, could not go ahead.
The parties came before the Federal Court on Thursday to discuss the next steps before a rescheduled three-week trial due to begin on October 9.
New defences and evidence will now be filed before the matter comes back before Justice Wigney on June 27.
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