An Iranian foreign ministry spokesperson, cited by Iran's ISNA news agency, said Iran would convey its response soon via Pakistan, which hosted the war's only peace talks and has since served as the main conduit for messages between the sides.
In an early morning social media post, US President Donald Trump gave no details of any specific proposal but said the war could end if "Iran agrees to give what has been agreed to".
He later told reporters in the Oval Office that Iran wanted to make a deal and "we'll see if we get there".
"We've had very good talks over the last 24 hours and it's very possible that we'll make a deal," Trump said.
"This is very simple: Iran cannot have a nuclear weapon," the president said.
A Pakistani source and another source briefed on the mediation confirmed information initially reported by the US media outlet Axios about a proposed 14-point one-page memorandum that would formally end the war.
The memorandum would be followed by discussions to unblock shipping through the Strait of Hormuz, lift US sanctions on Iran and agree curbs on Iran's nuclear program, the sources said.
"We will close this very soon. We are getting close," said the source from Pakistan.
Reports of the possible agreement caused global oil prices to plunge, with benchmark Brent crude futures falling 11 per cent to about $US98 a barrel.
Global share prices also leapt and bond yields fell on optimism of an end to a war that has disrupted energy supplies.
In his morning post, Trump said: "Assuming Iran agrees to give what has been agreed to, which is, perhaps, a big assumption, the already legendary Epic Fury will be at an end, and the highly effective Blockade will allow the Hormuz Strait to be OPEN TO ALL, including Iran."
"If they don't agree, the bombing starts, and it will be, sadly, at a much higher level and intensity than it was before," Trump added.
Hours earlier, Trump paused a two-day-old naval mission to reopen the blockaded strait, citing progress in peace talks.
Iran's Revolutionary Guards responded by saying that if US "threats" had ended, passage through the strait would be possible under new terms it was putting in place.
The White House, the State Department and Iranian officials contacted by Reuters did not immediately respond to requests for comment.
The source briefed on the mediation said the US negotiations were being led by Trump's envoy Steve Witkoff and son-in-law Jared Kushner.
If both sides agreed on the preliminary deal, that would start the clock on 30 days of detailed negotiations to reach a full agreement.
The full agreement would include the US lifting sanctions and releasing frozen Iranian funds, Iran and the United States lifting competing blockades on the Strait of Hormuz and some curbs on Iran's nuclear program, with the aim of a pause or moratorium on Iranian enrichment of uranium.
While the sources said the memorandum would not initially require concessions from either side, they did not mention several key demands the US has made in the past, which Iran has rejected, such as curbs on Iran's missile program and an end to its support for proxy militias in the Middle East.
The sources spoke of potential curbs on future Iranian enrichment of uranium but made no mention of Iran's existing stockpile of more than 400kg of it, already enriched to near weapons grade, which the US has previously demanded it give up before any end to the war.
Iran's Foreign Minister Abbas Araqchi, visiting China, made no mention of Trump's latest remarks but said his country was holding out for "a fair and comprehensive agreement".
with AP
