The former New Mexico Governor and his team held meetings in Moscow this week with Russia's leadership over the basketball star and ex-US marine Paul Whelan.

Both imprisoned Americans, who the US State Department classify as wrongfully detained, have been reported to be at the centre of potential prisoner exchange between Russia and the US.

However, the US State Department said the 74-year-old's trip was not coordinated with the US Government and he should not have travelled to Russia as a private citizen.

"Our concern is that private citizens attempting to broker a deal do not and cannot speak for the US Government, and we have urged private citizens not to travel to Russia, owing to the dangers that they would face," State Department spokesperson Ned Price said.

He added that staging such meetings outside the proper diplomatic channels could "hinder" the release of Griner and Whelan.

An unnamed official from within the administration of US President Joe Biden told media outlet CNN that anyone "who's going to Russia is going as a private citizen and they don’t speak for the US government."

Richardson has worked to secure the release of several Americans across the world as a Government official and through his organisation, the Richardson Center for Global Engagement.

He initially became involved in the case at the request of Griner's family in May and Cherelle Griner, Brittney's wife, said that they were "encouraged to hear" about the meetings.

In a statement to CNN, Griner said: "We've asked Governor Richardson and the Richardson Center to help us, and have been working with them for a while.

"We are encouraged to hear that they are having meetings in Moscow."

Kremlin spokesman Dmitry Peskov did not offer much of a comment on the subject.

"There were no meetings at the Kremlin," he told reporters on a conference call.

"I have nothing to tell you on this subject."

Several news outlets have reported that the Richardson Center have declined to comment.

The United States Olympic and Paralympic Committee chief executive Sarah Hirshland told reporters that there is no update on Griner's release.

Griner travelled to Russia to play for UMMC Ekaterinburg in the country’s domestic league during the Women’s National Basketball Association's off-season.

The Phoenix Mercury star was arrested on February 17 on drug possession charges after she entered Russia with vape cannisters containing cannabis oil.

Diplomatic efforts to free her have been made difficult due to the collapse of relations between the US and Russia following the invasion of Ukraine.

Griner was sentenced to nine years in a Russian prison last month.

Biden has called her detention "unacceptable" and promised to "tirelessly and pursue every possible avenue" to free Griner and Whelan.

Griner is currently appealing her nine-year sentence.

Whelan was sentenced to 16 years in prison in 2020 on espionage charges.