Mary Jane Binks, the Ottawa lawyer representing Williams' wife, said her client will ask to take the matter to the country's highest court.
"We're going to be seeking leave to appeal to the Supreme Court of Canada," Binks told The Canadian Press.
The move came after the Ontario Court of Appeal set aside a sweeping publication ban on the divorce proceedings in a ruling released Tuesday.
However, it allowed the ban to remain in effect for 14 days to give the former colonel's wife time to challenge the decision if she wished.
The ban, imposed by a lower court judge at the request of Williams's wife, forbids publication of her name, address, employer, income and medical information. It also covers a deal the couple signed about six weeks after Williams was charged with two counts of first-degree murder in the deaths of two eastern Ontario women.
Williams, once a rising star in the military and commander of Canadian Forces Base Trenton, was sentenced to life in prison in October 2010 after pleading guilty to the murders of Cpl. Marie-France Comeau and Jessica Lloyd.
He was also convicted of two sexual assaults and dozens of fetish break-ins. The Canadian Forces stripped him of his rank after his conviction and, in a rare move, burned his uniform.
Binks had argued that opening up the proceedings to the public would cause her client more harm than she has already experienced.
The ban was challenged by a coalition of news agencies, including the Ottawa Citizen, CTV, CBC, Global TV and the Ottawa Sun, who made their arguments before the Appeal Court last November.
In its 28-page decision, the court appeared to sympathize with the former colonel's wife.
"On the unchallenged evidence, the respondent is yet another victim of Williams' depravity," it said.
But the lower court judge erred in granting the sweeping ban, it added.
"The motion judge correctly identified the applicable legal principles," the ruling said. "However, the evidence cannot support her conclusion that the orders were necessary to prevent a serious risk to the proper administration of justice."
However, the court also ruled that some details about Williams's wife will remain under wraps, such as her social insurance number, date of birth, bank account numbers and certain medical information.
Richard Dearden, who represents the media groups, called the ruling an "important decision for freedom of the press."
"There's a real public interest in knowing how the court is going to divide assets, like Mr. Williams' military pension, and what's going to be left over for Mr. Williams' victims to seek to enforce any judgments they will get against him in their lawsuits against him," he said in an interview.
Two of Williams' victims — Laurie Massicotte and a woman whose name cannot be disclosed under a publication ban — have filed lawsuits against him and his wife.
Both have alleged in their statement of claim that Williams secretly and fraudulently transferred assets to his wife in March 2010 after he was criminally charged.
The claims, which have not been proven in court, were vigorously denied by Williams' wife in her statements of defence.
Dearden said the media groups could oppose a leave application to the Supreme Court of Canada.
Note to readers: This is a corrected story. An earlier version contained the incorrect word 'process' instead of 'press' in para 16.Suggest a correction