The chief executive of the Swedish firm which owns the Stena Impero said he had been informed that the vessel may be released later on Sunday.
"We have received information now this morning that it seems like they will release the ship Stena Impero within a few hours," Erik Hanell, chief executive of Stena Bulk told Swedish public broadcaster SVT.
"So we understand that the political decision to release the ship has been taken."
Iran detained the Stena Impero tanker in the Strait of Hormuz on July 19. The vessel had switched off its GPS locator, in contravention of international regulations, and was sailing into the strait in a wrong traffic pattern.
It was entering the strait from the southern route, which is an exit path, increasing the risk of an accident
Moreover, Stena Impero had not heeded any of the warnings from the Iranian Ports and Maritime Organization.
The UK oil tanker was reportedly also polluting the Persian Gulf waters heavily by dumping crude oil residue.