U.S. special representative to Iran, Brian Hook, reportedly emailed the captain of the Adrian Darya 1 about sailing the vessel to a country that would impound it on behalf of Washington.
The ship, which until recently was known as Grace 1, has been at the center of a diplomatic dispute between Iran and Western powers for several weeks.
The current whereabouts of the Iranian oil tanker is unknown, with reports suggesting it appears to have turned off its transponder in the Mediterranean west of Syria on Tuesday.
Reports of the cash offer first appeared in the Financial Times on Wednesday and have since been confirmed by the State Department.
"We have conducted extensive outreach to several ship captains as well as shipping companies warning them of the consequences of providing support to a foreign terrorist organization," a State Department spokesperson told AFP news agency on Thursday.
The State Department was not immediately available to comment when contacted by CNBC.
The U.S. blacklisted the Iranian oil tanker last week. The ship was temporarily detained by British authorities in Gibraltar in July after it was suspected of moving oil to Syria — a violation of European Union sanctions.
It was released last month after Tehran gave assurances about its destination. The U.S. justice department sought to block the release and issued a warrant to seize the ship.
A Treasury Department statement released late last month claimed Adrian Darya 1 was being used to transport 2.1 million barrels of Iranian crude to Syria.
The Financial Times reported that Hook sent an email to the ship captain, before imposing sanctions on the oil tanker.
"I am writing with good news," Hook said in the message, adding President Donald Trump's administration would be prepared to offer several millions of dollars to sail the ship somewhere the U.S. could seize it.
The Indian ship captain, Akhilesh Kumar, reportedly did not respond to the emails.
Citing the Financial Times' initial report, Iranian Foreign Minister Mohammad Javad Zarif said: "Having failed at piracy, the U.S. resorts to outright blackmail."
"Sounds very similar to the Oval Office invitation I received a few weeks back. It is becoming a pattern," Zarif added.