Cops Investigating New Video, Suspicious Man Near Nancy Guthrie's Home 1 Week Before Abduction

New video's surfaced in the search for Nancy Guthrie's kidnappers ... a man in Tucson with a goatee, who creepily approached a doorbell camera one week before Nancy was taken, and TMZ has learned cops are giving it a hard look.

The video was originally posted January 23 on Ring's Neighbors app, and it shows the guy intentionally backing up to the front door of a home about 6.5 miles from where Savannah Guthrie's mother lives.

The man clearly didn't want to be seen, but the camera still got a good shot of him as he rang the doorbell around 5 AM. The homeowner who posted the vid says the would-be intruder fled when their dogs started barking.

A high-ranking law enforcement source, connected to the investigation, tells TMZ ... the FBI and Pima Co. Sheriff's Dept. are aware of this video, and they're treating it as a potential lead.

The dark-haired individual does have facial hair that seems similar to the person seen in the FBI-released images captured by Nancy's doorbell camera.

Although that person was wearing a knitted ski mask, you can still see a goatee or beard underneath the material.

As we reported, the cops are asking residents within a 2-mile radius of Nancy's home to check security cameras for anything suspicious during the entire month of January ... as you know, Nancy was reported missing on February 1. This particular video is making the rounds on social media, so citizens are answering the call.