"The case has been referred to the Minister by the Court under the Extradition Act.
That process is required by the Act is cases such as this," her spokesman said.
"With that in mind, it wouldn't be appropriate to comment further."
The man's lawyer did not respond to the Herald.
An extremely tight suppression order prevents the Herald from publishing the man's name, age, location, occupation, marital status, immigration status in New Zealand, nationality and ethnicity.
The order also prevents publication of his alleged victim's name or any details that could identify her.
The man was arrested by New Zealand police last August on suspicion of killing his former partner in Switzerland 15 years ago. No charges have been laid but he could face manslaughter or murder charges if he is extradited.
The arrest came after an international search involving Interpol, New Zealand police and Swiss authorities.
Swiss police allege the man fled the country after killing the woman in her apartment.
Judge Paul said while all evidence Swiss police had linking the man to the murder was circumstantial - it could be inferred by that evidence at a trial that he was involved.
He said there was a "very strong case" against the man and a the probability of conviction was "certainly a likelihood".
