The American basketball star has been held in Russia for a month.
Ms Griner was arrested in February after Moscow airport officials found cannabis oil in her luggage while she was returning to the US.
She was wrongly imprisoned and should be released.
If she is convicted, she could face up to 10 years in prison.
The US State Department said a consular official spoke to the man on the margins.
A spokesman said that Griner was doing well and can be expected during difficult times.
Citing unnamed government officials, state-owned Russian news agency TASS is reporting that Russia wants to trade Ms Griner for Bout, a convicted arms trafficker in the US.
Bout was extradited to the US in 2008 after being arrested in Thailand, where he was accused of trying to sell weapons to the rebels.
He was sentenced to 25 years in a New York prison.
Russian authorities claim that a Sniffer dog led them to search the carry-on luggage of Griner.
Russian officials only confirmed her imprisonment in the second week of March, after the incident took place on 17 February.
The US and Women's National Basketball Association urged Americans to leave Russia because of the conflict in Ukraine.
US and WNBA officials have made little headway in their efforts to get her released.
The US and Russia still have diplomatic channels open for negotiations.
Last month, a US citizen and former Marine, who was serving a nine-year sentence for assault in Russia, was released from prison.
The US released a Russian pilot who had been sentenced to 20 years in prison for drug dealing.
The Office of the Special Presidential Envoy for Hostage Affairs is a section of the State Department that helps secure the release of Americans held hostage or wrongly imprisoned abroad.
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