But the government indicated it would resist that approach, suggesting in court on Tuesday that the matter wasn't ready for trial.

Outside court, Mr Eastman's solicitor Sam Tierney from Ken Cush & Associates, said Mr Eastman looked forward to having his case heard as quickly as possible so he could get on with his life.

"He's obviously spent the last, close to 30 years, fighting for freedom. In the context of what is a human rights application he looks forward to having this matter determined as quickly as possible," Mr Tierney said.

The case launched in 2015 after Mr Eastman, 73, was released from custody following a judicial inquiry into his conviction for murder.

After a trial in 1995, Mr Eastman was found guilty of murdering police chief Colin Winchester outside his house on January 10, 1989.

The former public servant spent 19 years in jail - 6860 days - before his release following the inquiry.

That inquiry found there had been a substantial miscarriage of justice, in part because flawed forensic evidence had gone in against Mr Eastman during the trial.

The ACT Supreme Court quashed the conviction and ordered a retrial.

At the end of a marathon retrial late last year, a second jury acquitted Mr Eastman of the murder and set the scene for a court battle over his compensation.

Lawyers for Mr Eastman say the government is liable under the territory's human rights act to compensate him for his alleged wrongful conviction and unlawful detention.

They say his imprisonment caused him deprivation of liberty, lost income, to suffer mental harm, damage to his reputation, and he had expended legal cost and time in fighting to reverse his conviction.

The government, in its defence, argues Mr Eastman's detention had been lawful and the human rights act did not give rise to any cause of action.

A registrar of the ACT Supreme Court said he would make orders in chambers setting a date for the court to hear the application to expedite the case.

Mr Tierney said that any circumstances in which someone spent time in detention where they shouldn't is a tragic outcome.

"The findings of the full court of the Supreme Court of the ACT have made it clear that miscarriages of justice have been visited on Mr Eastman, and we would like to think the government would make that right."

Questioned about the possibility of an out of court settlement, Mr Tierney said it was a matter for the government as the defendant in the proceedings.

"I don't think I can comment on what they may choose to do or not do."

Mr Eastman was not present in court.

Barrister Tony Bartley SC is briefed to appear in the case.