Potentially big development in the Nancy Guthrie abduction … our law enforcement sources say whoever kidnapped her from her Arizona home is also from the Tucson area.

Multiple sources involved in the investigation tell TMZ … the operating theory is that the ransom notes were written by the kidnapper, and those notes provide clues on where the abductor lives.

TMZ has focused for several days on the alleged kidnapper’s choice of media outlets to receive the letters. The first letter was sent to 2 Tucson TV stations and TMZ. The second letter was sent to only one of the Tucson stations.

Our law enforcement sources believe the person who wrote the ransom note was very familiar with the local stations … so much so that it leads them to believe the Tucson area is the abductor’s home.

As we reported, the kidnapper’s promising to return Nancy to Tucson within 12 hours of receiving the $6 million ransom … which means they’re currently somewhere within a 700-mile radius of Tucson.

There were 2 ransom deadlines, both of which have passed … even though ‘TODAY’ host Savannah Guthrie tried reaching out to the kidnapper and offered to pay up.

Our sources say the images the FBI released Tuesday of the apparent kidnapper were just obtained by authorities … the FBI wasn’t holding on to the images before releasing them. The feds got them and immediately blasted them out publicly.

Nancy was taken against her will on Feb. 1, and she has a pacemaker and needs daily medication.