Earlier, CNN, citing sources, reported that US President Joe Biden supported a plan to exchange Bout for American basketball player Brittney Griner and Paul Whelan.
“I hope these are not some empty words - and compromises on this issue will be found,” she said.
Bout's wife added that she talked with her husband on Tuesday, July 26, the conversation was about the health of the Russian.
Greiner was detained on February 18 at Sheremetyevo Airport on suspicion of trying to illegally import banned substances into Russia.
Her luggage was checked using X-ray equipment and found vapes (cartridges for an electronic heating system) with cannabis oil.
Earlier, Deputy Foreign Minister of Russia Sergei Ryabkov spoke about the possible exchange of Greiner for Bout.