The family of a Winnipeg woman who is believed to have been killed by accused serial killer Shawn Lamb say police have told them her remains are likely buried in the city dump.

Family members of Tanya Nepinak are now calling on police to search the Brady Road landfill until the 31-year-old woman's remains are recovered.

Tanya Nepinak, 31, went missing in September 2011 in Winnipeg. Police believe she was slain by Shawn Lamb, who is also accused of killing two other women within the past year. (Family photo)

"Nobody would want their family member or their loved one to be there. That's no final resting place for anybody," Vernon Mann, the father of Nepinak's two children, told CBC News on Tuesday.

Lamb, 52, was charged in June with three counts of second-degree murder in the deaths of Nepinak, Carolyn Sinclair, 25, and Lorna Blacksmith, 18.

Police have recovered the bodies of Sinclair and Blacksmith, but the body of Nepinak — who went missing in September 2011 — has yet to be located, despite numerous searches.

Mann said homicide investigators told him and other members of Nepinak's family almost two weeks ago that they believe Nepinak's body was dumped in a garbage bin which was then transported to the municipal landfill.

"They kind of have the approximate location of where everything is being dumped [from] that time," Mann said.

The family held a special ceremony for Nepinak at the Brady Road landfill last week, Mann said.

"It's really, really difficult, just knowing that she was under the ground that we were on and that it was just garbage everywhere," he said.

"It angered me to know that she was there and nothing was being done about it."

No decision made on search

Winnipeg police have not confirmed if they will scour the dump for Nepinak's body. Mann said he fears there will not be a search.

"They said between half a million and $1 million to do the search, and there would be a less than one per cent chance of finding anything," he said.

Vernon Mann, who is the father of Nepinak's two children, says Winnipeg police should have already started searching in the landfill for her remains. (CBC)

But Mann said family members don't care how much money is involved, as they won't give up until Nepinak is resting in a place of peace and respect.

Police should have started searching in the dump for Nepinak's body already, he added.

"We can't take no for an answer … that's their task to be done," Mann said.

"There's no 'maybes' or 'we'll see.' As far as we're concerned, it has to be done."

Police officials told CBC News that money is not an issue in this case, but investigators are consulting outside agencies, including the FBI, the province's medical examiner's office and the University of Manitoba's anthropology department, on whether they should launch a search of the landfill.

An announcement on the matter could come within a week, according to police.