Secretary of State Antony Blinken said Sunday that the U.S. is "actively engaged" with Russia in discussions over a prisoner swap to return American prisoners Brittney Griner and Paul Whelan.

Appearing on CBS News' "Face The Nation," Blinken said negotiations with Russia were ongoing.

"...We did put a significant proposal on the table many months ago. And since then, we've been engaged repeatedly, in any way that we can to try to advance it and to look to see if there are different permutations that could achieve what we're trying to achieve, which is to get our people home," Blinken said.

"Brittney Griner, Paul Whelan -- we're engaged in that on a regular basis. And it's my determination that we bring our people home. We will not stop until we do."

Griner is a professional basketball player who has been detained in Russia since February for possessing a small quantity of cannabis oil. Griner was transferred to a penal colony after being sentenced to nine years in prison.

Whelan is a former Marine who has been detained in Russia since 2018 after being convicted of espionage charges. He was sentenced to 16 years in prison by a Russian court in 2020.

Russian media has said that the state is looking for a one-to-one exchange. When asked about which prisoner would be chosen in that case Blinken did not go into details but said, "My efforts, the efforts of the entire administration are to bring both Paul and Brittney home."

While Moscow said that the chances of a prisoner exchange were growing, the State Department responded with less optimism.

"We have made a substantial offer that the Russian Federation has consistently failed to negotiate in good faith," Vedant Patel, a state department spokesperson, said at a Nov. 18 press conference.

Patel said that Russia's "failure to seriously negotiate on these issues in the established channel, or any other channel for that matter, runs counter to its public statements."

Viktor Bout, a Russian arms dealer, has been the speculated American exchange prisoner. Bout is serving 25 years after being convicted for conspiring to sell weapons to a Colombian terrorist organization that intended to kill Americans.

Blinken said that the U.S. will continue to put forward proposals to negotiate with the Kremlin on an exchange.

"...The proof will be in the pudding. We have to see if the engagements that we've had the discussions that we have produced an actual result. That's the most important thing but we are not resting on the laurels of having put forward a proposal some months ago, we've been actively engaged over these many months to try to move things forward," said Blinken.