Alavija, now 43, was sentenced to life with a 20-year non-parole period after being convicted of Ms Neumann's 1993 murder. Sources have revealed Alavija will face a Parole Board hearing later this month.
The disappearance of Anna Rosa Liva and Karen Williams are not connected to the Neumann murder - Alavija was not in Coober Pedy when both vanished.
Former Major Crime Detective Sergeant Mick Standing, who arrested Alavija, said he felt his non-parole period was "somewhat lenient''.
"It was one of the most brutal murders that I ever investigated,'' he said.
"She was alive when he threw her down the mineshaft and he lied all the way through our inquiry and the trial.
He has made several attempts to have his custodial sentence transferred to Croatia over the past decade.