An Australian chef has killed his girlfriend, dismembered her and boiled parts of her body before taking his own life, police say.

Marcus Volke (28) was fleeing officers who had come to his Brisbane apartment after reports of a foul smell when he took his own life.

Officers discovered body parts of Volke's girlfriend in a pot on the stove, while other parts of the Indonesian woman's mutilated body were found in garbage bins outside the apartment, according to local media.

Police are still to formally identify the body.

The couple had moved into the recently opened apartment complex in the wealthy riverside suburb Teneriffe just weeks ago, according to reports.

Volke had met his girlfriend while they were both working as chefs aboard international cruise ships. He had recently returned to Australia, his mother said.

"He was happy and he was coming home for Christmas, everything was normal," Dorothy Volke told the Courier-Mail from her home in Victoria.

Police said they were trying to establish the exact time of death.

They arrived at the apartment on Saturday night when other residents in the complex said a "rotting meat" smell had pervaded the area.

Volke then fled through a glass door and leapt over a balcony and hid in an alleyway where he killed himself.

Resident Courtney Reichart told the Australian Broadcasting Corporation (ABC) that she first noticed the smell on Wednesday and it got worse each day.

"On Saturday when I came out for a walk, it made your eyes water, it made you want to be sick," she said.

"The smell it was like as if somebody had put out some dog food or red meat and left it out for a few days."

"It makes you feel sick that that poor girl sat there for however many days and we've been walking past, living our lives and thinking 'hmmm what's that smell', but you don't put two and two together. You don't think that a bad smell equals a murder."

Ms Reichart had met the couple a number of times, telling the ABC that they were a "normal couple" and the girlfriend was "gorgeous".

Volke was originally from the Victorian city of Ballarat, where his funeral will be held.