According to his family, Michael R. White, 46, from Imperial Beach, California, was due to return from Iran where he was visiting his girlfriend on July 27, but never boarded his plane, the Times reported.
The Iranian-run outlet based its report on a former Iranian prisoner who said he met the American in Vakilabad Prison in the city of Mashhad back in October a year ago.
"All I know is that he is alive and they were putting in a request for a consular visit by the Swiss", she told the newspaper.
She shortly filed a missing-person report with the State Department, prompting the Department of Homeland Security to contact her.
Three weeks ago, State Department officials told her that White was being held at an Iranian prison.
She said she is anxious about his health, because he has had cancer and suffers from asthma.
After an Iranian news agency overseas reported that another American has been incarcerated in Iran, the New York Times confirmed the news by speaking to his Family. "I just want to see him home safe and sound", Joanne White said by phone.
The State Department told his mother they had put in a request for a consular visit by the Swiss embassy, which represents the interests of the United States in Iran since diplomatic relations were severed almost 40 years ago after the hostage crisis. "I know he was visiting his girlfriend".
"We are aware of reports of the detention of a USA citizen in Iran", a State Department spokesperson told the Washington Free Beacon on background. "Due to privacy considerations, we have no additional information to provide at this time", the official said.
In May 2018, the US withdrew from a nuclear pact with Iran and reinstated sanctions against the country. The State Department advises Americans not to travel to Iran "due to the risk of arbitrary arrest and detention".
Word of White's detention comes amid an already tense relationship between the US and Iran.
Iran is now holding at least three other US citizens, including Siamak and Baquer Namazi, and Princeton professor Xiyue Wang, in prison. Two of them are of Iranian descent while the other American citizens have been missing in Iran for over a decade.
The last time Iran released USA citizens from its prisons was when the nuclear agreement took effect in January 2016.