Hawker was sentenced to life imprisonment after sexually assaulting and stabbing 15-year-old Vanessa Woodman on the grounds of a Wellington high school in February 1997.
He was 18 at the time.
He was released on parole in December 2011, but was recalled in July 2012 after being found in possession of internet pornography, a recently released report by the Parole Board said.
In June, Hawker reappeared before the board after completing the Special Treatment Unit Rehabilitation Programme (Sturp) and a psychiatric assessment.
He accepted during his earlier release he had not engaged appropriately and was "emotionally disconnected", the report said.
"Mr Hawker himself initially put it down to his inadequate communication skills, but he agreed that his difficulties related more to his openness and honesty with respect to what was happening at the [release facility] than to his ability to communicate with staff."
A psychological report presented to the board found that his "emotional expression" had improved following the completion of Sturp.
At a separate meeting earlier this month, unnamed victims told the board of their concerns if Hawker was to be released, the report said.
They said his accessing pornography shortly after being first released on parole "reflected his sexual deviance which was also apparent in his index offending".
"In their view he remains a risk to women. He showed no empathy. In their view, if he is released he will reoffend," the report said.
However, the board said Hawker had completed an intensive programme to address issues behind his offending and a psychological assessment referred to his insight into risk factors that could lead to future offending.
The board said it believed temporary release to a facility was preferable to a prison-based reintegration scheme.
A Corrections Department spokeswoman would not say if a final decision had been made to release Hawker to the facility.
Hawker was due to appear before the Parole Board again in six months' time.
