"We can highly appreciate the role of both the United Arab Emirates and Saudi Arabia, which traditionally try to make a significant contribution to such processes," Peskov told the Izvestia newspaper.
When asked whether these states can contribute to the exchange of someone for US citizen Paul Whelan, the official said that "if necessary, the secret services will continue their work."
Griner, a WNBA player, was arrested earlier this year at Sheremetyevo airport, when Russian customs officers found cannabis oil in her luggage. Griner said she was aware that possession of drugs is banned in Russia, adding that she did not intend to violate the law. She was sentenced to nine years in prison and a fine of 1 million rubles ($16,576) in August.
Russia released Griner from prison in exchange for the United States releasing Bout on Thursday. The latter was serving a 25-year sentence in the United States for alleged arms dealing. Bout strongly denied the charges, with Moscow also saying that his arrest in Thailand and subsequent extradition to the US was a "kidnapping" of a foreign national by Washington.