The Iranian tanker Adrian Darya 1, formerly known as Grace 1, was halfway between Syria and Cyprus when it turned off its automatic tracking system on Monday.
The tanker was released by the Gibraltar authorities on 18 August despite requests from Washington to continue detaining the vessel.
Assessments made by independent ship tracking service Tankertrackers.com show the Adrian Darya 1 still located 60 miles off the coast of Syria.
It is believed the Iranians may attempt to unload oil in ship-to-ship transfers onto smaller tankers working out of the Syrian port of Tartus.
This would contravene UN sanctions on Syria and sanctions designed to prevent the Iranians selling oil.
On Wednesday, the US Treasury Department released a report identifying a network of vessels and facilitators who have moved millions of dollars of oil from Iran to Syria and the terrorist organisation Hizballah.
This has been controlled by the Iranian Revolutionary Guard Corps Quds Force which the United States also designated a terrorist organisation earlier this year.
The report accuses Iran of using 12 named tankers to smuggle oil out of Iran often using ship-to-ship transfers where two ships come alongside and transfer oil at sea to hide the origin of the oil.
On 30 August, the US Treasury Department designated the Adrian Darya 1 and the ship’s captain Akhilesh Kumar as providing support to terrorism.
The Financial Times is reporting that four days prior to this the US offered millions of dollars to the ship's captain if he sailed to the port where the tanker could be impounded.
Open-source information is also indicating that, on Wednesday, a US RC-135U Combat Sent reconnaissance aircraft was searching the area in the eastern Mediterranean where the Adrian Darya 1’s was last reported.
It is believed that the Iranian oil tanker has yet to offload any oil to the Syrians.
On Tuesday, Iran announced it would release seven of the crew from the UK-flagged Stena Impero.
It is possible the Iranians are connecting the release of this ship's crew with the successful delivery of oil to Syria.
Meanwhile, the Type 23 frigate HMS Kent should arrive in the Straits of Hormuz in the next few days with Type 45 destroyer HMS Defender a few days behind.
The presence of two frigates and destroyer in the Gulf will bring the UK naval presence in the Gulf back to the Armilla Patrol levels during the 1980s tanker war.
Hear Christopher Lee's in-depth analysis on this story on the latest Sitrep.