The U.S. president said Wednesday that he'd like to sit down and make a "fair deal" with China on trade that would eliminate the need for the massive tariffs he's put on the nation.
Xi on Thursday said he looks forward to meeting with Trump at the G20 in Argentina, according to China's state media.
Sterling jumped nearly two per cent on the report despite London and Brussels officials' reservations.
It comes ahead of a key meeting between Mr Trump and China's President Xi Jinping at the G20 summit this month.
The meal would give the two leaders more time to talk and create an atmosphere more conducive to negotiations, the sources said.
A Bloomberg report said the U.S. president had asked officials to begin drafting a potential trade agreement with China, citing unnamed sources. Despite tariffs, he said US economic growth expanded in the last two quarters and was on track to hit the Administration's 3 percent target for the full year.
Trump told reporters before leaving the White House that the USA is "close to doing something" with China to ease the ongoing trade war between the two countries. While Beijing is open to striking a deal that narrows the trade deficit, officials have resisted Trump's other demands - including an end to subsidies for strategic industries, a stop to forced technology transfer and more competition for state-owned enterprises.
At the same time he noticed that in case all goes well with trade talks with Beijing, the USA may lift tariffs against China.
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"Frankly, the principal culprit is China", he said. Beijing would be unwilling to risk jeopardising its improving relations with Pyongyang and as a result had "very few tools to work with", he said. "We talked about many subjects, with a heavy emphasis on Trade", the United States president tweeted.
"They are maybe too complex to be solved in just one meeting", he said.
Earlier Friday, the Chinese foreign ministry said Trump and Xi had an "extremely positive" phone conversation Thursday. He has also emphasized the need to reduce the USA trade deficit with China.
Lu Xiang, a specialist on United States affairs at the Chinese Academy of Social Sciences, said that Beijing had been preparing for a "worse than the worst" confrontation with the USA, and added that any further escalation would be fatal to an already highly volatile U.S. stock market. At a campaign rally in Columbia, Missouri, he later said "they want to make a deal".
"Given his [Trump's] poor track record on policy credibility in the past year, we'd better not hold out too much hope", Lu said. Earlier this year, the Trump administration imposed tariffs on $250 billion worth of Chinese goods, prompting Beijing to retaliate.
Analysts said Trump could be simply trying to sooth investors and boost the stock market in the run up to the midterm elections by teasing a deal.
"I spoke with President Xi (Jinping) yesterday".
Both countries presidents have expressed optimism in resolving their issues.