Robert Samuel Geeves and his wife Anne Margaret Geeves, both 62, have pleaded not guilty to the murder of Ms Haigh and will face a joint trial later this year.
On Friday in the NSW Supreme Court, Robert Geeves' lawyers filed an application for a judge-alone trial to be conducted without the presence of a jury.
Anne Geeves is set to join him in the application and a Supreme Court judge will decide the matter in July.
The pair were arrested and charged at a property in the Riverina town of Harden in May.
Ms Haigh was reported missing on June 19, 2002, after failing to return to her home at Kingsvale where she and her six-month-old son had been living with the couple.
Police were told the pair dropped the young mother at Campbelltown station on June 5 and she intended to travel by train to Mt Druitt in western Sydney to visit her sick father in hospital.
Later that night, money was withdrawn from her bank account at a Campbelltown ATM.
A coronial inquest in 2011 found Ms Haigh died as a result of homicide or other misadventure in June 2002.
In 2020, a formal review of the case was conducted under the Homicide Squad's Unsolved Homicide framework and Strike Force Villamar II began a fresh investigation.
NSW Police announced the reward for information about the cold case had been increased from $100,000 to $1 million in April.
A video message from Ms Haigh's heartbroken mother Rosalind Wright was also released.
"I know in my heart that she would never have left her son," she said in the video.
The mother's body has never been found.
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