Guthrie went missing from her home in Tucson, Arizona, in early February. The FBI is offering a reward up to $100,000 for information leading to her location.
A ransom note sent to US media outlets in the wake of the kidnapping of Nancy Guthrie, the mother of presenter Savannah Guthrie, said she had died, according to reports.
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It was reportedly the second of two notes sent to news organisations following her abduction, with the other demanding millions of dollars for the 84-year-old's release.
CNN and Kold News, an Arizona television station, said they were aware of the contents of the second note but that they had initially agreed not to share details so as not to compromise the investigation.
Mary Coleman, an evening news anchor at Kold News, said the FBI told the station it was taking the note seriously.
"Law enforcement tells us the two letters are believed to be sent by the same person," she wrote in a post on social media.
The second note said the kidnappers had not intended to kill Guthrie but that she had died shortly after she was abducted, CNN reported.
Guthrie went missing from her home in Tucson, Arizona, in early February. Police said she had last been seen on the evening of 31 January, close to her residence in the Catalina Foothills neighbourhood.
Authorities later released images and video footage showing a masked individual outside Guthrie's home who appeared to tamper with the front door camera.
The FBI is offering a reward up to $100,000 for information leading to Guthrie's location "and/or the arrest and conviction of anyone involved in her disappearance".
The agency has described the suspect as male, around 5’9” to 5’10”, with an average build. It said he can be seen wearing a black, 25-litre "Ozark Trail Hiker Pack" backpack in the door camera footage.