It is reported by CNN, citing sources.
It is noted that the proposal to Russia was sent in June.
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.