The Phoenix Mercury center was arrested February 17th with vape cartridges containing cannabis oil in her luggage.
Griner was sentenced to nine years in a penal colony on August 4th on drug smuggling and possession charges.
On Monday - Labor Day in the United States - the Women's National Basketball Players Association issued a plea on social media for all US union members to sign a Change.org petition in support of Griner.
United States President Joe Biden has said Griner is being "wrongfully detained."
Diplomats for Russia and the US have reportedly discussed a prisoner swap to bring Griner and fellow American Paul Whelan home in exchange for the release of convicted arms dealer Viktor Bout.
The number one overall pick in the 2013 WNBA Draft, Griner is a seven-time All-Star and two-time Defensive Player of the Year with career averages of 17.7 points, 7.6 rebounds and 2.8 blocks in 254 games.