Earlier this week, authorities said they had yet to identify a person of interest or suspect in the case.
They are offering a reward of $50,000 (£36,000) for information.
Nancy Guthrie was discovered missing when members of her church grew concerned when she did not attend Sunday services.
Authorities say that early on Sunday morning, a doorbell camera in her home was disconnected and removed. At about 02:28 local time, the app connected to her pacemaker, a implanted cardiac device, was disconnected from her phone.
FBI Special Agent Heith Janke has said the bureau is looking into a potential ransom note sent to several media outlets.
Authorities on Friday said they were “aware of a new message regarding Nancy Guthrie”. They are “inspecting the information provided in the message for its accuracy”.
Janke said the note “had facts associated with a deadline with a monetary value they were asking for”, NBC News reported.
A presenter for a local CBS News affiliate told the BBC that her channel had received the “message” but did not detail its contents.
According to news website TMZ, which reportedly received one of the letters, the kidnappers were demanding millions of dollars’ worth of the cryptocurrency, which is popular with criminals and often difficult to trace.