News Ltd reports that Tony Byrne would make legal history as the first family member of a victim to seek to take over a criminal appeal.
Mr Byrne's lawyers are drafting grounds for him to lodge an application and seek leave to appeal to the High Court following the state's top prosecutor, Director of Public Prosecutions Lloyd Babb SC, ruling out any appeal by his office.
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"We are certainly going to give it a go," Mr Byrne, 76, said.
"I have the strength and power to do this as long as I have support, and I have plenty of support."
The NSW Court of Criminal Appeal last month overturned Wood's conviction for the 1995 murder of his live-in lover, 24-year-old model Caroline Byrne.
In 2008, Mr Wood, then 46, was found guilty of murdering the model by "spear throwing" her off a cliff at The Gap, a notorious Sydney suicide spot at Watsons Bay, late on the night of June 7, 1995.
The former chauffeur to stockbroker Rene Rivkin was jailed for at least 13 years after the jury rejected a claim that Ms Byrne, whose mother had killed herself in 1991, had jumped off the cliff.
After his acquittal, Mr Wood was released from Goulburn jail on February 24 after spending three years behind bars.
