The family says they have been spurred into action by the latest media reporting of the case which suggests the only evidence against Mr Keogh was the discredited testimony from a former forensic scientist.

They say other evidence against Keogh is "cogent and available" and a retrial would provide certainty over his guilt or innocence.

Their lawyer Greg Griffin told reporters on Wednesday that the family wanted the Director of Public Prosecutions Adam Kimber to take "all steps necessary for an immediate retrial of Mr Keogh".

"So that the South Australian public and all those involved in the prosecution of Mr Keogh have certainty as to whether Mr Keogh is guilty or not guilty of the charge of murder," he said.

Ms Cheney, 29, was found in the bath at her Adelaide home and Mr Keogh, who was her fiance at the time, was eventually charged with her murder.

A jury in his first trial failed to reach a verdict but in a second trial he was convicted and jailed for at least 25 years.

But he always maintained his innocence and had his conviction overturned in 2015 with the Court of Criminal Appeal ruling that the jury had been misled by pathologist Colin Manock and called for a third trial to be held.

However, Mr Kimber decided not to proceed, with the state government in July also awarding Mr Keogh an ex-gratia payment of $2.57 million to settle the matter and avoid further litigation.

Mr Griffin said the Cheney family wanted the Attorney-General Vickie Chapman to explain the basis for the payment and release the advice the government relied on.

He said the family's only hope for "closure" in the matter was a retrial.

"The problem was that they were not consulted," he said.

"After the full court directed a retrial, the government did not meet with the Cheney family except to call them into a meeting to tell them they weren't going to retry the matter."

"The full court said in its judgment that there was circumstantial evidence that a properly directed jury could use to convict and the position is that we believe the trial should have taken place."

South Australian Premier Steven Marshall said the question of a retrial was not a matter for the government.

"The government has been very clear about our reasons for the payment that was made and if there is going to be a further trial we'll await to see what the out of that trial is," he said.

Australian Associated Press