There’s a major new development in the Nancy Guthrie case ... authorities now reportedly believe her kidnapping may have stemmed from a burglary gone wrong.

According to AZFamily, citing an inside source, Savannah Guthrie's mother is believed to have been abducted during a botched home invasion -- instead of a carefully planned abduction.

What's more ... the source also tells the outlet there is belief among investigators that Nancy could be alive.

The theory comes on the heels of the FBI's announcement that DNA was recovered from a glove found near the scene ... the glove appears to visually match the gloves worn by the alleged perpetrator. As you know, the masked intruder was caught on a doorbell camera lurking around Nancy's home just before she was abducted on February 1.

The FBI plans to run the DNA profile through its CODIS database in hopes of identifying a match tied to a convicted offender.

Meanwhile, Savannah shared another emotional plea on Instagram Sunday night, saying she hasn’t lost hope and urging whoever has her mother to “do the right thing.”

As for the alleged ransom notes sent to TMZ and other media outlets ... investigators have yet to identify the person or persons who wrote them -- and no suspects have been named in the case.