Nancy Guthrie, 84, was last seen at her Arizona home on January 31 and was reported missing the following day.
Authorities say her blood was found on the front porch.
Purported ransom notes were sent to news outlets, but two deadlines for paying have passed.
The Federal Bureau of Investigation released surveillance videos of a masked person wearing a handgun holster outside Guthrie's front door in Tucson the night she vanished.
A porch camera recorded video of a person with a backpack who was wearing a ski mask, long pants, a jacket and gloves.
Pima County Sheriff Chris Nanos told The Associated Press on Monday that the 25-litre Ozark Trail Hiker Pack backpack was the only clothing item that had been "definitively identified".
"This backpack is exclusive to Walmart and we are working with Walmart management to develop further leads," Nanos said.
The suspect's clothing "may have been purchased from Walmart but is not exclusively available at Walmart," the Pima County Sheriff's Department said in a statement Monday.
"This remains a possibility only."
Investigators on Sunday announced that a glove discovered near the Guthrie home has been sent for DNA testing.
The FBI said that it received preliminary results on Saturday and was awaiting official confirmation.
The development comes as law enforcement gathers more potential evidence and as the search for Guthrie's mother heads into its third week.
Authorities previously said they had not identified a suspect.
The FBI said the suspect in the surveillance footage is a man about 175cm tall with a medium build.
Authorities have expressed concern about Nancy Guthrie's health because she needs vital daily medicine.
She is said to have a pacemaker and to have dealt with high blood pressure and heart issues.
