The U.S. government and his family have denied the charges against Hekmati.
On Monday, the semiofficial Isna news agency said the case would be retried.
The report quoted state prosecutor Gholam Hossein Mohseni Ejehei as saying, "There was an appeal on his verdict. The Supreme Court found shortcomings in the case and sent it for review by an equivalent branch" in the court system.
The report did not elaborate.
Last month Hekmati's mother visited him in prison and met with Iranian officials. Some saw this as a sign that Iran might show moderation in the case.
A lawyer for the family, Pierre Prosper, welcomed word of the retrial. Prosper said he is "waiting for official confirmation, but we are pleased with reports coming out of Tehran."
Prosper said the family is looking forward to working with the Iranian government. The lawyer said an appeal has been in the works and progress in the case may be unrelated to the escalating pressure on Iran over its nuclear program.