The US has offered Russia a prisoner swap in a bid to free two Americans, including basketball star Brittney Griner.
Reports have suggested that US officials will offer to swap Russian arms trafficker Viktor Bout, who is serving a 25-year prison sentence in the United States, as part of a deal.
Mr Blinken did not go into detail about the terms of the proposed deal to release Ms Griner, and another American, Paul Whelan.
The basketball star was arrested on drug-related charges at a Moscow airport in February and testified on Wednesday at her trial.
Russian authorities arrested her after they found her in possession of vape cartridges containing cannabis oil in her luggage.
She testified at her trial Wednesday that she had no criminal intent in bringing them into the country and packed in haste for her return to play in a Russian basketball league during the WNBA's offseason.
Mr Whelan, a corporate security executive from Michigan, was sentenced in 2020 to 16 years in prison on espionage charges.
He and his family have vigorously asserted his innocence and the US government has denounced the charges as false.
“We put a substantial proposal on the table weeks ago to facilitate their release,” Mr Blinken said.
“Our governments have communicated repeatedly and directly on that proposal, and I'll use the conversation to follow up personally and, I hope, to move us toward a resolution."
Mr Blinken said he would also press Russia’s Foreign Minister Sergey Lavrov on the need for allowing grain exports from Ukraine.
The proposed deal comes after a prisoner trade in April secured the release of jailed Marine veteran Trevor Reed who was arrested in Russia in 2019.
Russia has for years expressed interest in the release of Bout, a Russian arms dealer once labelled the “Merchant of Death”. He was sentenced to 25 years in prison in 2012 on charges that he plotted to illegally sell millions of dollars in weapons.