The report did not identify the prisoners and the person in Iran was speaking to The Associated Press on condition of anonymity since he was not authorized to publicly speak to the media.
Rezaian is a dual Iran-US citizen who was convicted of espionage in a closed-door trial in 2015.
Washington Post spokeswoman Kris Coratti told the AP that she could not confirm any change in Rezaian's case.
A report by the semi-official ISNA news agency quoted a statement from the Tehran prosecutor's office as saying the inmates were freed "within the framework of exchanging prisoners." It did not elaborate.
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The family of one of the US prisoners received unofficial word from Iran that their relative was being released today, according to a person close to that family who spoke on condition the family not be identified.
Iran was seeking a number of detained Iranians in exchange for the Americans.
Iran was known to be holding four Americans. It was unclear who was being released, but the four were: Rezaian, who was born in California and holds both US and Iranian citizenship. He was convicted in closed proceedings last year after being charged with espionage and related allegations.
He was originally detained with his wife in July 2014. She was released on bail in October 2014. Rezaian was the Post's Tehran correspondent and was accredited to work in the country by the Iranian government.
Former US Marine Amir Hekmati of Flint, Michigan. He was detained in August 2011 on espionage charges. His family says he has lost significant weight and has trouble breathing, raising fears he could contact tuberculosis.