Detectives have spoken to the man they believe killed New Zealand nurse Michelle Beets in Sydney.

The Daily Telegraph in Sydney reported yesterday that the man - who was connected to Ms Beets through her job at Royal North Shore Hospital - met police in the days after the 57-year-old was stabbed to death. He was one of dozens of people interviewed as part of their investigation, the Telegraph said.

The newspaper said police were now awaiting the results of forensic testing.

Ms Beets, who worked as the hospital's emergency department nursing manager for 10 years, was killed on the doorstep of her home at Chatswood in Sydney's north as she returned from work.

The paper said a collection of floral tributes had been laid on the front lawn of Ms Beets' home.

"Michelle was like a mother to all of us at work," one woman, who asked not to be named, said.

The house was closed up with its power box taped up after forensic officers examined it.

Ms Beets' Auckland-based brother Marty said the family had a sense of closure after his sister's funeral last Friday.

"We just want him to pay for what he has done," Mr Beets said of the killer.

He thanked the police working on the case and hoped it would only be a matter of time before his family got some "good news".

The Telegraph said police were continuing to sift through items found at the nearby Artarmon Waste and Recycling Centre after it was closed and searched for two days last week.