The Pakistani source said a report by US media outlet Axios on the proposed memorandum was accurate.
"We will close this very soon. We are getting close," the Pakistani source said on Wednesday.
In April, Pakistan hosted the war's only peace talks so far, and it has continued in that role of mediator.
Reports of the possible agreement to end the war caused global oil prices to plunge, with benchmark Brent crude futures falling more than eight per cent to about $US100 a barrel.
The White House and Iranian officials did not immediately respond to requests for comment.
US news channel CNBC quoted a spokesperson from the Iranian foreign ministry as saying Tehran was evaluating a 14-point US proposal.
Axios reported that the White House believed it was closing in on a one-page memorandum to end the war with Iran.
The report came hours after US President Donald Trump paused a three-day-old naval mission to reopen the Strait of Hormuz.
The Axios report said the US expected Iranian responses on several key points in the next 48 hours.
Among other provisions, Axios said, the deal would involve Iran committing to a moratorium on nuclear enrichment, the US agreeing to lift its sanctions and release billions of dollars in frozen Iranian funds, and both sides lifting restrictions around transit through the Strait of Hormuz.
The one-page, 14-point memorandum of understanding was being negotiated between US envoys Steve Witkoff and Jared Kushner and several Iranian officials, Axios said.
In its current form, the memorandum would declare an end to the war and the start of a 30-day period of negotiations on a detailed agreement to open the strait, limit Iran's nuclear program and lift US sanctions, Axios said.
Earlier, Trump announced a pause to "Project Freedom", a mission he announced on Sunday to guide ships through the blocked strait.
The mission had failed to bring about any significant resumption of traffic through the waterway, while provoking a new wave of Iranian strikes on ships in the strait and on targets in neighbouring countries.
In announcing he was pausing the mission, Trump cited "great progress" in negotiations with Iran, without giving further details.
"We have mutually agreed that, while the Blockade will remain in full force and effect, Project Freedom (The Movement of Ships through the Strait of Hormuz) will be paused for a short period of time to see whether or not the Agreement can be finalized and signed," Trump wrote on social media.
Trump had launched the naval mission to guide ships through the strait after saying he was likely to reject Iran's latest proposal.
The Iranian offer, made last week, had called for setting aside discussion of nuclear issues until after the war ended and the shipping dispute was resolved.
In comments on a visit to China on Wednesday, Iranian Foreign Minister Abbas Araqchi made no mention of Trump's latest remarks, but said Tehran was holding out for "a fair and comprehensive agreement".
Iran has effectively shut the strait to all shipping apart from its own since the United States and Israel launched the war on February 28.
In April, Washington imposed its own separate blockade of Iranian ports.
Trump's Project Freedom mission to use the US Navy to open the strait failed to persuade merchant ships that it was safe, while provoking new attacks from Iran.
Iranian drones and missiles hit several ships in and around the strait, including a South Korean cargo vessel that reported an explosion in its engine room.
Tehran also repeatedly struck targets in the UAE.
10°C