Denyer pleaded guilty to stabbing and strangling three young women in the Melbourne bayside suburb of Frankston in 1993.
He was sentenced to life in jail with no parole but in a later appeal, a non-parole period of 30 years was set.
The adult parole board on Wednesday told the families of his victims his application for parole was refused.
Brian Russell, the father of 17-year-old victim Natalie Russell, said it was the best news he had heard in 30 years.
"I'm pretty happy at the moment, put it that way," he told 10 News on Wednesday.
"He has no remorse whatsoever and he's still proud of what he did."
In a seven-week killing frenzy, Denyer stabbed and strangled Elizabeth Stevens, 18, Debbie Fream, 22, and Natalie, 17.
Victorian MP David Limbrick, who was in a relationship with Natalie at the time of her death, said waiting to hear about Denyer's parole was traumatising.
He said he would push to reform the parole process.
"Now is the time to have a conversation about how we manage this going forward," Mr Limbrick said on Wednesday.
"We can't just keep going through this every few years."
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