Griner, a two-time Olympic gold medallist and Women's National Basketball Association (WNBA) star, was sentenced to nine years in prison in Russia on drug charges on August 4th in a ruling US President Joe Biden called "unacceptable".
"Quiet diplomacy is under way and it should bear fruit if Washington follows it, and not fall into propaganda through media hype to score points before an election," said Ivan Nechayev, a spokesman for the Russian foreign ministry, referring to the US midterm elections in November.
The Kremlin had previously said that US officials were undermining efforts to secure a prisoner swap by resorting to "megaphone diplomacy" over the case.
Washington has offered to exchange Russian arms trafficker Viktor Bout for Griner and former Marine Paul Whelan, sources familiar with the situation have told Reuters.
Whelan, who holds American, British, Canadian and Irish passports, was sentenced in 2020 to 16 years in jail after being convicted of spying. He denied the charge.
Griner, who had been prescribed medical cannabis in the United States to relieve pain from chronic injuries, was arrested on February 17th at Moscow's Sheremetyevo airport with vape cartridges containing hashish oil in her luggage.
Cannabis is illegal in Russia for both medicinal and recreational purposes.
Griner, who pleaded guilty to the charges, said she had made an honest mistake by inadvertently packing her vape cartridges as she rushed to catch her flight to Russia.
