The Trump-Xi meeting would mark the first since the countries trade relations started to strain with the introduction of import taxes earlier this year.
The meal would give the two leaders more time to talk and create an atmosphere more conducive to negotiations, the sources said.
The comments appeared to be aimed at shoring up confidence among entrepreneurs who generate China's new jobs and wealth amid complaints Beijing is dragging its feet on economic reforms and reining in the dominance of state industry.
Trump sounded very optimistic about reaching a trade deal with China, or else, he warned, he was ready to impose a trade tariff of 25 per cent on another United States dollars 267 billion worth of Chinese products. He backed out on a deal congressional Democrats said they struck with Trump to provide legal status to young undocumented immigrants. "I am very cautious regarding the outcome of their meeting".
"The two countries' trade teams should strengthen contact and conduct consultations on issues of concern to both sides, and promote a plan that both can accept to reach a consensus on the China-US trade issue", Xi told CCTV state television.
"They are maybe too complex to be solved in just one meeting", he said. "I spoke with President Xi (Jinping) yesterday".
On the other hand, China chided the U.S. for indulging in "trade bullying".
On Wednesday, US Secretary of State Mike Pompeo said China was probably Washington's biggest long term security challenge and the United States was engaged in a "multi-pronged effort.to convince China to behave like a normal nation on commerce " and respect worldwide law. "They very much want to make a deal", Trump said.
President Donald Trump's steep tariffs on billions of dollars worth of Chinese products don't seem to be particularly effective at re-balancing trade. He said trade would be a topic when he gets together with Xi over dinner.
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.
China has repeatedly questioned the US's sincerity in trade talks, wary of agreeing to something only to have Trump change his mind. "The result is that the trust deficit widens".
Trump noted that significant progress has been made in resolving differences between the United States and China.
China's economy grew by a slower-than-expected 6.5 percent in the 3 months to September.
"As the president said, we would like to talk to them about it, but they may not be ready".
White House economic adviser Larry Kudlow said at an event in Washington that Trump and Xi might be able to break the logjam on issues during the summit.
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