The Russian official said he expected a positive result from the prisoner exchange negotiations between the US and Russia.
The prospect of Bout coming back to Russia is being strengthened, and the moment will come when we will get a concrete agreement, according to the Russian deputy foreign minister.
The first public remarks by an American or Russian official that Bout would be part of a swap to return Griner to the U.S. were made by the Russian official.
Forbes reported in May that the U.S. offered to swap Bout for someone else.
Brittney is doing well and was transferred to the IK-2 penal colony in Mordovia, Russia.
After discovering a cannabis product in her luggage as she traveled to play in the country's basketball league, the Russian authorities arrested her. She received a nine-year prison sentence in August but the US considers her to be wrongly imprisoned. She was transferred to a colony last week after her appeal to shorten her sentence was turned down. Outside of Moscow is the Mordovia penal colony.
An exhibition of Bout's artwork was on display in the Russian parliament. Bout was sentenced to 25 years in Illinois for conspiring to kill Americans and selling weapons to terrorist groups.
The arms dealer who could be swapped for Griner is not known. The story was reported by the Associated Press.