According to ABC News, Anne Cameron, 79, was reported missing from an aged care facility near Port Douglas, north of Cairns, on Tuesday.
Acting Inspector Ed Lukin said police and the SES had found clothing and a walking stick with the woman's name on it near a crocodile-infested creek.
"We've also located some biological matter which we believe to be human remains, but those items are currently being tested in Cairns," he said.
He said police and the SES would continue to search the area in the hope she could be found alive.
"Because of the proximity of these items and this unknown material located near this creek bank, we cannot rule out the possibility of a croc attack.
"We still hold our hope that we will find this missing person alive, of course as the days progress that option will diminish, and as time goes by we will continue to reassess our searching options."
Police said Ms Cameron suffers from dementia.
Results of the forensic tests are expected later today or tomorrow morning.
State Emergency Service area controller Sean McGuinness said the search is proving to be difficult.
"The search area is relatively flat, however the environment with the mangroves and the swamp area, it is quite hard to get through that area," he said.
"The teams are persevering, they understand what we need to try and achieve and basically try and assist police to get some information about the situation."
'She's only been here eight or nine days'
The Department of Environment and Heritage Protection said wildlife officers were assisting police with the search for a crocodile in the area.
Surveillance will be conducted on water and on foot tonight.
A number of traps are available in the area, but not likely not to be deployed until tomorrow.
Ozcare, the company that runs the aged care facility, declined to comment.
Fellow resident Judith Wright said she saw Ms Cameron walking towards the facility's administration building shortly before 4:00 on Tuesday, the day she disappeared.
"She didn't appear to be worried about anything," she said.
Ms Wright said she was very upset when she heard Ms Cameron was missing.
"I was very shocked, we got along quite well even though we'd only known each other a few days," she said.
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