The ship was released from detention off Gibraltar about five weeks after it was seized suspected of breaching EU sanctions by shipping oil to Syria.
Ship tracking data on Saturday showed the ship had switched destination and was heading to Turkey instead of southern Greece.
However, a Turkish official told Reuters earlier on Thursday that the Iranian tanker had not entered Turkish waters.
The latest tracking data showed the ship was currently between the coasts of Turkey and Cyprus, heading west.
On Monday, IRIB news agency quoted an Iranian government spokesman as saying that Iran had sold the oil from the Adrian Darya and the vessel’s owner will decide on its next destination.