A suspect in the killing of Sydney nurse Michelle Beets has been led from his home by homicide detectives and is expected to face further questioning.

The 57-year-old New Zealand-born nurse manager from Sydney's Royal North Shore Hospital was viciously stabbed to death on the doorstep of her Chatswood home on April 27.

Witnesses reported seeing a man wearing a green top and carrying a backpack running from the scene around the time of the killing.

Investigations into the killing led police to a Lane Cove apartment last week which they spent three days searching.

The apartment's occupant, a former colleague of Ms Beets, has openly denied being linked to the killing.

He has already been questioned by police over the killing.

The 48-year-old man, who has a military background and speaks with an American accent, says he believes he is a suspect because he is a foreigner.

About 6pm today police led the man away from his apartment, the Nine Network reported.

Footage showed a man with yellow material covering his head, being led to a car by three detectives.

A police spokeswoman was unable to provide any information on the events.

So far, police have set up various crime scenes as part of their investigations into Ms Beets's death, and have also sifted through about 300 tonnes of rubbish at three Sydney tips in search of evidence.

- AAP