Whelan (L) was detained on espionage charges in December 2018, while Griner (R) was found guilty of smuggling and storing narcotics this year.
The United States and Russia have been discussing the release of basketball star Brittney Griner and ex-marine Paul Whelan through special channels.
The US had submitted a serious proposal for consideration, Russian state-owned RIA Novosti news agency reported on Monday, citing a top US diplomat.
Elizabeth Rood, charge d'affaires of the US embassy in Russia, was quoted as saying that the US had not received a "serious response" back from Russia.
The two countries have been discussing a deal that could see Griner and Whelan return to the US in exchange for Russian weapons trafficker Viktor Bout, who is serving 25 years in prison in the US on a 2012 conviction.
No deal has materialised amid heightened tensions between the two countries.
Victor Bout, an alleged Russian arms smuggler, is likely to be swapped by the US in exchange for basketball star Brittney Griner and former marine Paul Whelan, both detained in Russia pic.twitter.com/iBoP829Lck
— TRT World (@trtworld) July 28, 2022
Brittney Griner
31-year-old US basketball star Brittney Griner was arrested at a Moscow airport in February for possessing vape cartridges with a small amount of cannabis oil.
The two-time Olympic basketball gold medallist and Women's NBA champion was in Russia to play for the professional Yekaterinburg team during her off-season from the Phoenix Mercury.
She was sentenced to nine years in a Russian penal colony and a fine of $16,590 (1 million rubles) in August after she was found guilty of smuggling and storing narcotics.
Griner said the banned substance was prescribed by a US doctor to relieve pain from her many injuries and pleaded guilty to the charges, but said she did not intend to use the substance in Russia.
The US has denounced her sentencing, with President Joe Biden saying it was "unacceptable", while Russian officials said US statements about the case showed disrespect for Russian law.
Griner was moved to a penal colony earlier in November despite repatriation efforts by Washington.
READ MORE: US furious as basketball star Griner moved to Russia penal colony
American basketball star Brittney Griner was arrested on drug charges in Russia. A former Pentagon official says Moscow will use the arrest to "blackmail" Washington during the war in Ukraine pic.twitter.com/xMMSCpKgii
— TRT World (@trtworld) March 7, 2022
Paul Whelan
52-year-old Paul Whelan, a former US Marine, was arrested in Moscow by Russia's Federal Security Service on espionage charges in December 2018.
Accused of receiving state secrets, Whelan's trial was heard behind closed doors at a Moscow court and he was sentenced to 16 years in prison in 2020.
Whelan denies the charges, insisting that he was framed while in Moscow for a friend's wedding when he took a USB drive from an acquaintance, thinking it contained holiday photos.
Whelan's family has complained in the past that he has been mistreated in prison and not received needed care.
Washington has repeatedly denounced his arrest and detention.
A security official at an auto parts company at the time of his arrest, Whelan holds US, Canadian, Irish and British citizenship.
READ MORE: Russia engaging in 'quiet' diplomacy with US on prisoner swap
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