Grace 1, carrying Iranian oil, was stopped by Royal Marines on 4 July, triggering a standoff with Tehran.
The vessel was due to be released, after Gibraltar’s attorney general indicated there would be no further order for its detention.
But the US request will be considered, with a court hearing set for 15:00 BST.
Gibraltar said the US application is based on a “number of allegations which are now being considered”.
The UK Foreign Office said it was unable to comment on the US request.
A spokesman for Gibraltar’s government also confirmed that police proceedings against all four members of the crew, including the captain – an Indian national – had ended.
The crew’s legal team told the BBC that police had said this was due to actions by the Iranian government, and that it was no longer in the public interest to proceed.
The crew of 28 are Indian, Russian, Latvian and Filipino and have spent 43 days in detention on board the ship.
The Grace 1’s captain said in a statement: “I am grateful and thankful for my release. And I am grateful to all who have facilitated my release in my legal team.”
The tanker was seized after the government of Gibraltar suggested it was heading for Syria, in breach of EU sanctions.
The Gibraltar authorities have since received assurances from the captain of the ship and Iran that Grace 1 was not going to Syria.
About 30 marines were flown from the UK to Gibraltar to help police detain the tanker and its cargo, at the request of the Gibraltar government.
The initial seizure of the tanker sparked a diplomatic crisis between the UK and Iran, which has escalated over recent weeks and saw the seizure of a British-flagged and Swedish-owned oil tanker, Stena Impero, in the Gulf.
It is clear from the Gibraltarian authorities that without the last minute US intervention the Grace 1 would have been released and on it way.
The hope was that this in turn would clear the way for the eventual release by the Iranians of the Stena Impero – the British-flagged vessel they seized in the Gulf.
The last-minute effort by the US Justice Department has certainly muddied the waters, raising more questions.
What grounds do they have for seeking to seize the vessel? And crucially how much co-ordination if any was there between the US, Britain and Gibraltar.
Or did Washington’s request come out of the blue?
On 19 July, the Stena Impero was seized by Iran’s Revolutionary Guard in the Gulf.
Last week, the UK announced it would join a US-led taskforce to protect merchant ships travelling through the key shipping route in the Strait of Hormuz.
Tensions between Iran and the West can be traced to the resurgence of another crisis – that over Iran’s nuclear programme.
Last year, Washington withdrew from a 2015 deal to limit the Iran’s nuclear activities, amid suspicion that Tehran was still trying to develop nuclear weapons. Something Iran has always denied.
Since then, US-Iran tensions have grown after Washington imposed – and latterly tightened – its sanctions against the country.
The UK and other European countries have said they remain committed to the deal.