According to four sources familiar with the matter, the agreement would extend the truce for another 60 days and allow traffic to flow through the strategic waterway while negotiators tackle difficult issues such as Iran's nuclear programme.
If approved by leadership in Washington and Tehran, it would amount to the biggest step towards peace since the conflict began on February 28. News of the possible agreement came after a round of tit-for-tat attacks between the two countries, the latest such incident since the ceasefire took effect in early April.
Trump had not yet approved the deal, the sources said. Iran has yet to comment on news of the proposed deal, which was first reported by Axios.
Iran's Tasnim news agency, citing a source close to the negotiating team, said the text of the agreement had not been finalised or confirmed.
"We're not there yet, but we're very close and we're going to keep on working at it," US Vice President JD Vance told reporters in Washington.
"I can't guarantee that we're going to get there, but right now I feel pretty good about it," Vance said.
The Trump administration has several times said a deal to end the fighting was close, only to have Iran dispute or downplay the claims.
The deal would specify unrestricted shipping through the strait and would require the US also lift its blockade of Iranian ports. The US would also lift some sanctions on Iranian oil sales.
The reports prompted oil prices to fall on hopes of a potential reopening of the Strait of Hormuz, a key transit route for roughly a fifth of the world's oil and liquefied natural gas supply.
Earlier, US Central Command said its forces had shot down five Iranian attack drones and struck a ground control station in the port city of Bandar Abbas that was about to launch a sixth. Kuwaiti forces then intercepted a ballistic missile fired towards the country, which hosts a large US base.
A US official also said no American aircraft were shot down near Bushehr, Iran, contradicting a report by Iran’s state television that a US aircraft had been downed there.
The incidents, while limited, highlighted the fragility of negotiations to turn the tenuous ceasefire into a lasting agreement to end the three-month-old war, which has killed thousands and upended global energy markets.
A US official, speaking on condition of anonymity, said the strikes were defensive and intended to maintain the ceasefire.
The Islamic Revolutionary Guard Corps said it had targeted the US base responsible for the Bandar Abbas attack, and that any repeat would lead to a "more decisive response", Tasnim news agency reported.
Kuwait condemned the attack and demanded that Iran immediately halt what it called a serious escalation.
The violence, the second flare-up this week, coincided with the Muslim holiday of Eid al-Adha celebrated across the region, where multiple countries have been caught up in the conflict.
Mediator Pakistan said its foreign minister, Ishaq Dar, would meet US Secretary of State Marco Rubio in Washington on Friday, although the significance of his visit was unclear.
Trump has repeatedly said an end to the war is close since mid-March, though the two sides have shown little public movement toward common ground. Iran has called for sanctions to be lifted, foreign assets to be unfrozen, and US forces to be withdrawn from the region. Washington has called for Iran to dismantle its nuclear programme, which Tehran says is for peaceful purposes.
Iran says any peace deal must also end US ally Israel's attacks in Lebanon, but that conflict shows no signs of flagging. Israel said it had targeted infrastructure of Iran-backed Hezbollah militants in the southern city of Tyre and had carried out a strike in the capital Beirut. Israel has displaced hundreds of thousands of people with a push deep into Lebanon in pursuit of Hezbollah. The Lebanese army said a strike had killed one of its soldiers.
WARNING TO OMAN
The US warned Oman not to get involved in any effort with Iran to impose a toll in the Strait of Hormuz, and Trump on Wednesday threatened to bomb the country, despite a history of economic and military ties between the two countries.
Treasury Secretary Scott Bessent said Oman's ambassador had told him there were no plans to impose such tolls.
Oman has not mentioned the idea of joint control of the strait with Iran, with which it says it has discussed freedom of navigation. Tehran expressed solidarity with Oman after what it called "US officials' threats".
