The elite force's spokesman also said the strait would not open unless the US met Iranian conditions under an interim ceasefire agreement that was struck in June before unravelling.
Those conditions include an end to the US blockade on Iranian ports, compensation and removal of sanctions.
Iran and Oman have held on-and-off talks for weeks about controlling traffic through the strait, which handled one-fifth of global oil and liquefied natural gas shipments before the war began in February.
Most shipping has since been shut down, driving global energy prices higher, as Iran and the US have tried to assert control over the channel, imposing separate blockades.
"An agreement with Oman over the Strait of Hormuz has not been finalised," the senior Iranian source told Reuters, adding that the talks were continuing on the details of an accord.
A spokesman for Iran's Islamic Revolutionary Guard Corps (IRGC) had said Iran and Oman had reached an agreement on their shares of the territory and revenues.
"The Strait of Hormuz belongs to Iran and the country of Oman ... We have been in negotiations with Oman for about a month, and we have reached results that are acceptable to both sides," Hossein Mohebbi said in comments published by Iranian state media.
"In these negotiations, agreements have been reached regarding the share of each country in the waters of the strait and the share of Iran and Oman in its revenues," he added.
It was not immediately clear at what stage of the negotiations the agreements had been reached.
Iran had said earlier this month that a deal on the strait was close.
Following talks on Tuesday between Iran and Oman, Omani Foreign Minister Badr Albusaidi said he was "hopeful we will soon announce a temporary corridor for the Strait of Hormuz and practical arrangements to restore safe navigation".
The IRGC accused the United States of seeking to obstruct Iran's negotiations with Oman and said this had caused an agreement to be delayed.
"If the United States stops obstructing and returns to the agreement, we can open the Strait of Hormuz within the framework of the agreement reached ... If the United States does not accept our conditions, the Strait of Hormuz will not be opened under any circumstances," Mohebbi said.
Although active hostilities between the US and Iran have largely subsided in recent weeks, diplomatic efforts to reach a peace deal have stalled, and continuing attacks on ships mean passage through the Strait of Hormuz remains perilous.
Iran announced a blacklist on Sunday of 45 ships in an apparent effort to stop ship-to-ship transfers used by Gulf energy producers to evade the Iranian blockade.
Some companies plan to stop using vessels added to the blacklist, sources said.
In an effort to tighten pressure on Iran's economy, the United States has threatened to punish countries that continue to do business with Iran, but said it would not impose penalties immediately.
The sanctions did not feature Chinese financial institutions suspected of facilitating oil exports from Iran that the US blockade has cut.
Iran denounced the US effort to isolate its economy as an act of "gross lawlessness," expressing confidence that many countries would not join the pressure campaign.
Oil prices fell for a third day, dropping more than 1.5 per cent, following signs of renewed efforts to seek a mediated end to the war that began on February 28 with US and Israeli strikes on Iran.
Secretary of State Marco Rubio told allies that the US did not expect to launch new strikes against Iran for now and would instead focus on other means of pressure, Axios reported on Tuesday.
