US investigators have reportedly been in touch with Mexican authorities about the disappearance of American news anchor Savannah Guthrie's mother, as the search stretches into a third week.

The sheriff's department in the US state of Arizona and FBI declined to confirm they had contacted authorities across the border to help trace Nancy Guthrie.

But her family has contacted a Mexican non-profit that works to find missing people in the region.

Investigators have been sifting through 40,000 leads since the 84-year-old was reported missing this month, but a breakthrough has eluded them despite emotional public appeals for help from her NBC presenter daughter.

US news website TMZ reported on Wednesday that the FBI had contacted authorities in Mexico, believing it was possible Guthrie could have been taken across the border.

ABC News cited law enforcement sources as saying the FBI had notified Mexican authorities of Guthrie's disappearance, although they had no evidence she had been taken across the border.

A Mexican security official told the New York Times the FBI had contacted officials in the state of Sonora, which shares a border with Arizona, to investigate an alleged "purchase" in the case, although that potential lead had apparently fizzled.

It is standard practice for federal investigators to talk with Mexican counterparts, especially in cases so close to the border, Fox News reports.

The Searching Mothers of Sonora, a Mexican non-profit dedicated to finding missing people in that state, often in cases linked to drug cartels, confirmed to CBS, the BBC's US partner, that it had been asked by a Guthrie family member to help the search.

There has been no suggestion from officials that Guthrie was abducted by narco-traffickers.

TMZ also said it had received a new ransom note via email demanding about $6m in cryptocurrency.

The outlet, which previously reported receiving another possible Guthrie ransom note, said it had forwarded the new email to the FBI.

Guthrie was last seen at her Tucson, Arizona, home on 31 January when a family member dropped her off there after an evening at her daughter's house nearby.

Investigators suspect she was abducted in the early hours of 1 February.

Arizona investigators say her family members have been ruled out as possible suspects.

On Tuesday, Pima County Sheriff Chris Nanos told the BBC that DNA evidence taken from a glove found near Guthrie's home had produced no matches in a FBI database.

The glove had appeared to match ones worn by a masked man captured on surveillance footage on the night Guthrie vanished.

Nanos said he was confident they would find her, whether it took "10 days, 10 months, or worse".

He also said that he believed Guthrie was being held somewhere close to her home.

Investigators are now using a device that might be able to detect Bluetooth signals coming from her pacemaker, law enforcement sources told CBS.

The sources said the tool, called a "signal sniffer", was mounted on a helicopter.

Guthrie's pacemaker was disconnected from her phone app on the night of her disappearance.