The information is not confirmed.
Griner was in a Russian prison for drug possession, which she admitted, for 10 months before being exchanged with a Russian arms dealer in early December.
The case received extremely high attention and her wife Cherelle appeared at the White House together with US President Joe Biden in connection with the release.
Vice President Kamala Harris and Secretary of State Antony Blinken also attended the performance.
Two Olympic golds with the USA
Griner did not show up and was taken to a hospital for examination.
In a social media post in December, Griner said she would return to Phoenix, a team she played for in 2021 and reached the WNBA Finals, a season in which she averaged 20.5 points.
32-year-old Griner, 206 cm tall, has two Olympic gold medals and a WNBA title as her main credentials.