The FBI did not specify how many ransom notes had been received, other than saying "several".
"This case continues to be investigated as a kidnapping-for-ransom case," the FBI said in the statement.
The Pima County Sheriff's Department is also investigating the case.
The department declined to comment on the notes on Wednesday but said it was taking every tip in the investigation seriously.
Tucson TV station KOLD has said it received two notes, one demanding millions in bitcoin in exchange for Guthrie's return and another that said she had died. TMZ also received a note.
Guthrie is the mother of longtime Today show host Savannah Guthrie.
Authorities believe she was kidnapped, abducted or otherwise taken against her will on February 1.
They found blood near the front doorstep of her home just outside Tucson, and the FBI later released surveillance videos showing a masked man on the porch that night.
Volunteers and search teams scoured the nearby desert terrain filled with cactuses, bushes and boulders in the weeks after she vanished.
A volunteer group recently conducted a search for her body near the Arizona-Mexico border.
