There is “no evidence” that the masked man captured on doorbell camera footage at Nancy Guthrie‘s Arizona home visited there before the day the 84-year-old is believed to have been kidnapped, the Pima County sheriff tells PEOPLE.

There had been reports on Monday, Feb. 23 that the man seen in the footage may have come to Nancy’s house before Feb. 1.

“There is no evidence to support that… and there is no evidence to support it was all on the same day,” Pima County Sheriff Chris Nanos tells PEOPLE on Monday. “It is speculative at best and remains part of an ongoing investigation.”

On Feb. 10, the FBI released photos and video of the masked person on Guthrie’s doorstep. They have not been confirmed to show activity from two different days, including on Feb. 1, when authorities believe she was abducted.

Nanos also addressed questions about whether the masked suspect may have returned on a different day.

“It could be accurate,” Nanos says about the masked suspect returning on a different day, because he’s not wearing a backpack or gun holster with a weapon in one of them. “We just don’t have evidence to support when each image was taken… There is no date or timestamp and we are still investigating it.”

The Pima County Sheriff’s Department also released a statement on Monday, emphasizing the same uncertainty.

“We are aware that doorbell images released earlier in the investigation depict a suspect in different stages of attire, including with and without a backpack. There is no date or time stamp associated with these images. Therefore, any suggestion that the photographs were taken on different days is purely speculative,” officials said.

“This remains an active and ongoing criminal investigation,” officials continued. “As with any investigation, conclusions will be guided by verifiable evidence and established facts. Speculation, without factual support, does not advance the investigative process.”

Guthrie vanished from her secluded Tucson, Ariz., home after she was last seen on Jan. 31. Since then, local, state and federal authorities have flooded the area, spending nearly a month combing the rugged desert terrain for any sign of her or clues that could lead investigators to answers.

Residents in Guthrie’s neighborhood were previously asked by the sheriff’s department to submit surveillance footage dating back to Jan. 1, with particular focus on two windows of time between Jan. 11 at 9 p.m. and midnight, and Jan. 31 between 9:30 a.m. and 11 a.m. Authorities specifically requested video showing cars, traffic, pedestrians or anything unusual.

The FBI later released footage and images of a masked, armed man tampering with Guthrie’s doorbell camera the morning of her disappearance, a development that generated over 20,000 tips. The suspect is described as a man approximately 5’9” to 5’10” tall with an average build.

Investigators determined from the footage that the individual was wearing an Ozark backpack, according to the Pima County Sheriff’s Department. Detectives are still working to identify other items seen in the video and where they may have been purchased.

Authorities have visited gun shops in the Tucson area, as the suspect appears to be wearing a gun holster that, Nanos previously said, “had some pretty unique characteristics.”

In addition to appealing to nearby residents, law enforcement has canvassed homes, businesses and government agencies for surveillance footage in an effort to trace where Guthrie may have been taken, locals and law enforcement involved in the case tell PEOPLE. Investigators continue to sift through “thousands of hours” of video collected from the greater Tucson area.

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Forensic work is also ongoing. DNA recovered from Guthrie’s home was analyzed, Nanos said on Feb. 17. Gloves discovered about two miles from the residence, one of roughly 16 gloves found during the search of the surrounding area, did not produce any matches in the national CODIS database, and did not match DNA collected from inside the home.

“There is additional DNA evidence that was found at the residence that is also being analyzed,” the PCSD said.

Authorities have detained and later released two individuals in connection with the investigation, the sheriff’s department previously confirmed.

Despite weeks of searching, investigators do not have a leading theory regarding motive, according to Nanos. However, authorities said they believe Guthrie was removed from her home against her will, and the sheriff previously told PEOPLE they have not ruled out the possibility that more than one person was involved.

As recently as Feb. 21, detectives and agents were again canvassing Guthrie’s neighborhood, though officials did not disclose what prompted the renewed activity.

Nancy’s children, Today co-host Savannah Guthrie, her sister Annie and her brother Camron, have repeatedly pleaded for her safe return. In a series of social media videos, they have addressed purported ransom notes sent to several media outlets and urged the public to come forward with information. Despite reports of ransom communications, neither the family nor law enforcement has confirmed whether the notes were legitimate or if any direct contact was made with the sender.

The sheriff has emphasized that no family members, including siblings or spouses, are considered suspects.

Two rewards remain available for information in the case: up to $102,500 through 88-Crime, the Pima County and Tucson affiliate of Crime Stoppers, and up to $100,000 offered by the FBI for information leading to an arrest.