The Victorian government is working on parole law changes amid calls to ban Denyer from ever reapplying after his request was knocked back earlier this year.
Denyer pleaded guilty to stabbing and strangling Elizabeth Stevens, 18, Debbie Fream, 22, and Natalie Russell, 17, in a seven-week period in the Melbourne bayside suburb of Frankston in 1993.
He was sentenced to life in jail with no parole, which was later reduced on appeal to a non-parole period of 30 years.
In May, the Adult Parole Board told the families of his victims that Denyer's application for parole was refused.
Premier Daniel Andrews admitted the board needed to engage much better with victims' families, and apologised to the loved ones of Denyer's victims.
"It's very clear to us … that this process has not been particularly well handled," he told reporters.
"The system has had 30 years to get ready for this day and sadly I don't think those families have been as well supported as they should have been."
Mr Andrews said the changes may create minimum periods between parole applications, or limit the number of times certain prisoners can apply.
They would likely target murderers and mass murderers, particularly those who do not participate in rehabilitation programs.
Similar legislation exists in Western Australia, which introduced new laws in 2018 to restrict parole for serial killers and mass murders.
Victorian Attorney-General Jaclyn Symes has met with the victims' families and said they welcomed her suggestion to build a "buffer" between applications.
"I teased this out with the family, and it's fair to say a minimum of five years would be our starting position," she said.
No time-line has been set for the legislative changes to come before parliament.
The Victorian coalition last month introduced a private members' bill to parliament to ensure Denyer could not make further bids for freedom.
Opposition criminal justice reform spokesman Brad Battin said the families of Denyer's victims deserved targeted legislation akin to that for Hoddle Street shooter Julian Knight and Russell Street bomber Craig Minogue.
"Anything that allows him to have an application for parole in the future is spitting in the face of the families," he said.
In 2018, the Andrews government changed the Corrections Act to specify that Minogue could not be released unless he is in imminent danger of dying or so incapacitated he is no longer a danger.
It mirrored previous legislation for Knight that was introduced by the Liberal Napthine government in 2014 and supported by the then-Andrews opposition.
Victorian MP David Limbrick, who was in a relationship with Ms Russell at the time of her death, questioned why the government had adopted a different approach for Knight and Minogue.
"If anyone's going to be on that list of people, Denyer clearly should be," he said.
"He's committed some of the most heinous crimes in the history of this state and the prospects for rehabilitation, as state Justice (Frank) Vincent said, were zero."
Mr Limbrick said the proposed reforms may not guarantee Denyer cannot re-apply for parole.
"There have been instances in the past where devious prisoners have engaged in these rehabilitation programs just to get parole and then have reoffended," he said.
"That doesn't really provide much comfort to me at all."
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