Presidents Xi and Trump held a phone conversation on Thursday, with the USA leaders saying the call had "a heavy emphasis on Trade".
The Trump administration says it's trying to pressure Beijing to make deep changes to its economic policies, accusing it of overseeing the theft of U.S. intellectual property and unfairly boosting Chinese companies through aggressive industrial programs.
"We've had very good discussions with China".
U.S. stocks could get a further boost when the latest data on nonfarm payrolls is released at 8:30 a.m.in Washington (12:30 p.m.in London).
The Bloomberg News report said it was unclear if Trump was easing up on demands that China has resisted, and it cited one person as saying intellectual property theft was a sticking point on a possible deal.
"This is pre-election hype created to make the markets happy; there is no imminent deal with China", Greg Valliere, the chief global strategist at Horizon Investments, told Business Insider.
The U.S.is on track to post its biggest foreign trade deficit in a decade, Market Watch reported.
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The United States has targeted $348 billion in Chinese products with tariffs, a move which saw Beijing lashed back with $153 million tariffs us goods.
"We do hope that China and the United States will meet each other halfway and work together in the spirit of mutual respect and equality", Li told Trump's fellow Republicans.
According to Chinese state media, Xi also said on Thursday that he hoped "China and the United States will be able to promote a steady and healthy relationship".
China's official Xinhua News Agency said that Xi accepted the call at Trump's invitation. "And I think it'll be a very fair deal for everybody, but it will a good deal for the United States", he said.
Just this week, the USA government struck at the heart of China's ambitions to become a global tech powerhouse by banning American companies from exporting parts and software to a major Chinese state-owned maker of computer chips. Earlier this year, the Trump administration imposed tariffs on $250 billion worth of Chinese goods, prompting Beijing to retaliate.
Washington introduced the duties in response to what it says are long-running, unfair trading practices by China, and Beijing has retaliated in kind.
Background: Trump and Xi are expected to meet at the G-20 summit on either November 30 or December 1. At a campaign rally in Columbia, Missouri, on Thursday night he said, "They want to make a deal".
He has also threatened to impose tariffs on a further $267bn worth of Chinese goods.