Their families say the Americans were just intrepid travelers out on a hike in northern Iraq's scenic, and relatively peaceful, Kurdish region when they were arrested on July 31, 2009.
The U.S. government has denied the charges against them and demanded their release. Their lengthy detention has added to tensions between the two nations over issues like Iran's disputed nuclear program.
After her release, Shourd said in an interview with the New York Times that the three inadvertently crossed the unmarked border because a guard of unknown nationality gestured for them to approach.
Shourd, from Oakland, California, has not disclosed any plans to return for trial. She did not immediately respond to an e-mail seeking comment on Monday. Samantha Topping, a publicist for the Americans' families, said they were aware of the reports but had no plans for immediate comment.
Iran has warned it will seize the $500,000 bail if she does not return. Who provided the bail money that was paid as part of a deal brokered by the Gulf Sultanate of Oman has never been clear.
Initially, Tehran accused the three Americans only of illegally crossing into Iran, but later added espionage charges. Authorities have given few details to support the accusations.
Tehran's chief prosecutor has claimed, without elaborating, that the Americans had "equipment and documents and received training."
The three Americans are graduates of the University of California at Berkeley. Shourd and Bauer had been living together in Damascus, Syria, where Bauer was working as a freelance journalist and Shourd as an English teacher. Fattal, an environmental activist, went to visit them in July 2009.
On Monday, eight international figures, including actor Sean Penn, American academic Noam Chomsky and retired Archbishop Desmond Tutu of South Africa, issued an appeal for Iran to release the two men. "The time for Shane and Josh's freedom is overdue and we implore you to allow them to go free and return to their families," the statement said.