Blinken said he would be pressing his Russian counterpart to respond in a conversation planned for the coming days.
Washington offered Moscow a deal to bring home basketball star Brittney Griner and former US Marine Paul Whelan weeks ago, Blinken said at a State Department news conference, and hoped to advance the process when he speaks to Russian Foreign Minister Sergei Lavrov.
Russia's foreign ministry said it had not been formally approached by Washington to set up a phone call, Tass news agency said later on Wednesday.
"There was a substantial proposal on the table weeks ago to facilitate their release," 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 move us toward a resolution."
He declined to say what the United States was offering in return.
News channel CNN reported Washington was willing to exchange Russian arms trafficker Viktor Bout, who is serving a 25-year prison sentence in the United States, as part of a deal to secure the release of the Americans.
A Russian lawyer for Whelan has previously said he believed Moscow wanted Bout to be part of a prisoner swap for Whelan.
Blinken declined to characterise how Moscow has so far reacted to the proposal, which he said had President Joe Biden's sign off.
Families of hostages and detainees have been increasing pressure on Biden, most recently in the case of two-time Olympic medallist Griner, who has been held since February.
Griner, who was detained at Moscow's Sheremetyevo airport - allegedly with vape cartridges containing cannabis oil in her luggage - was in court on Wednesday in the latest hearing of her ongoing trial on drug charges. The next hearing is set for August 2.
"From a legal point of view, an exchange is only possible after a court verdict," Griner's lawyer in Russia, Maria Blagovolina, said in a statement to Reuters.
Whelan was sentenced in 2020 to 16 years in prison in Russia, accused of spying. He denied the charges and said he was set up in a sting operation.
The plight of American detainees has gained visibility after Griner's arrest and the release in April of former US Marine Trevor Reed at a time when US relations with Moscow are at their worst in decades over Russia's invasion of Ukraine.
Reed was detained for three years. In a prisoner exchange, the United States commuted the prison sentence of Russian pilot Konstantin Yaroshenko, who was convicted of cocaine smuggling.
Blinken said his planned call with Lavrov, the first such conversation between the two diplomats since before Russia's invasion of Ukraine in February 24, will not be a negotiation about the war.
The White House declined to go into the details of the US proposal but said that Biden directed his national security team to pursue every avenue to bring Griner and Whelan home safely.
"We believe that this is a serious proposal and we want the Russians to take it seriously as well," White House spokesman John Kirby said.
Kirby declined to say if Washington was offering a prisoner swap but said the administration was balancing the "need to get these Americans home" with US national security and "that we're not encouraging hostage-taking in the future."