Shinzo Abe, the Japanese prime minister, is set to offer himself as a mediator amid the escalation of tensions between the United States and Iran.
Mr Trump landed in Tokyo on Saturday for a four-day visit during which Mr Abe will discuss the proposal with him, and seek his consent.
The Japanese leader is considering a visit to Tehran net month to mediate with President Hassan Rouhani, according to media reports in Japan, and a final decision may depend on the results of his talks with Mr Trump.
Mohammad Javad Zarif, the Iranian foreign minister, visited Japan earlier this month.
Shortly before his Japan trip Mr Trump ordered 1,500 extra US troops, along with fighter jets, reconnaissance aircraft, and missile defence batteries to the Persian Gulf.
The Pentagon called it a "defensive" deployment intended to protect US troops in the region from Iran. Mr Zarif said the new US deployment "threatens international peace".
For the first time the US also publicly accused Iran of carrying out a sabotage attack against oil tankers off the coast of the UAE, and said it had evidence Iran planned to load cruise missiles onto small ships, and use Shia militias to attack US forces in Iraq.
As tensions escalated Mr Trump also used national emergency powers to sweep aside objections in Congress and push through £6.3 billion in arms sales to US allies Saudi Arabia, the UAE, and Jordan.
Both Democrats and Republicans had been holding up the arms sales because of concerns over the civilian death toll caused by Saudi and UAE airstrikes in Yemen, as well as the murder of Washington Post journalist Jamal Khashoggi by Saudi operatives.
Mike Pompeo, the US secretary of state, said the threat from Iran justified the use of emergency powers and sidelining Congress.
He said: "These sales will support our allies, enhance Middle East stability, and help these nations to deter and defend themselves from the Islamic Republic of Iran."
Chris Murphy, a Democrat senator, said: "President Trump is only using this loophole because he knows Congress would disapprove.
"There is no new 'emergency' reason to sell bombs to the Saudis to drop in Yemen, and doing so only perpetuates the humanitarian crisis there."
Japan has longstanding ties with Iran and opposed Mr Trump's decision to withdraw from the 2015 Iran nuclear deal. Before US sanctions on Iran, Japan was a major importer of Iranian oil.
Mr Abe first visited Iran in a personal capacity in 1983 and has continued links with the country's leadership.
Reacting to the idea of him mediating Akihisa Nagashima, a former Japanese defence minister, said: "This is what we call quiet diplomacy."
It was unclear how Mr Trump would react to the offer, and Mr Abe would have to overcome the hurdle that no Japanese prime minister has visited Tehran officially since before the Islamic Revolution.
An Iranian foreign ministry spokesman said Mr Rouhani had invited Mr Abe "a while ago" but suggested such a visit was unlikely in the near future.
On Monday Mr Trump will become the first head of state to meet Emperor Naruhito since he ascended to the Japanese throne this month.
During his largely ceremonial visit to Japan he will also attend a sumo competition, play golf with Mr Abe, and discuss trade issues.
Hours after arriving Mr Trump warned Japan over its "substantial edge" in trade and joked: "Maybe that's why you like me so much."
The two countries are locked in trade talks and the visit is part of Mr Abe's ongoing charm offensive aimed at fending off US tariffs.
Mr Trump has been threatening potentially devastating tariffs on Japanese cars unless he wins concessions, including for US farmers.
Speaking to Japanese business leaders, including executives from Toyota, Nissan and Honda, Mr Trump warned it was time to "address the trade imbalance".
He also called on Japan to buy more US military equipment because "the world is changing".