The Russian Foreign Ministry said talks were underway via a channel set up by President Biden and Russian President Vladimir Putin when they met in Geneva in June last year.
Russian Foreign Ministry spokesman Ivan Nechayev said Thursday that negotiations about an exchange began after Foreign Minister Sergei Lavrov confirmed last week that Russia was willing to talk.
"Instructions were given to authorized structures to carry out negotiations," Nechayev said. "They are being conducted by competent authorities," he told journalists in Moscow on Thursday, state media reported.
The Biden administration has been under pressure to secure Griner's release after her arrest at Moscow's Sheremetyevo International Airport in February. She was carrying two vape cartridges with cannabis oil, containing less than a gram of the substance, which is banned in Russia.