"And I think it'll be a very fair deal for everybody, but it will a good deal for the United States", he said.
Shi also said he thought China had only a limited role to play on the North Korea issue.
The meal would give the two leaders more time to talk and create an atmosphere more conducive to negotiations, the sources said.
"Trump said the two countries have a chance to make a fair deal". 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.
US-China talks have made little progress since May, when Trump put a stop to a deal that would see China buy more energy and agricultural goods to narrow the trade deficit.
"We are getting much closer to doing something", Trump said.
Trump has railed against the USA trade imbalance with China since his presidential campaign, and his administration has grown increasingly vocal about calling out alleged corporate espionage and intellectual property theft by Chinese entities.
China has repeatedly questioned the US's sincerity in trade talks, wary of agreeing to something only to have Trump change his mind. At time of writing, Trump is scheduled to meet Chinese authorities in a few weeks, with the potential outlook of a breakthrough in prolonged trade tensions representing an investment opportunity for financial markets to further unwind of United States dollars positions.
Isaac Boltansky, a policy analyst at the research and trading firm Compass Point, told Business Insider that the complexity of the issues the U.S. and China are discussing - intellectual property rights, Chinese laws restricting how United States companies can operate in the country, and more - make a deal hard.
Trump had earlier said on Twitter that he held a "very good" conversation with the Chinese president "with a heavy emphasis on trade".
His administration has demanded that Beijing make sweeping changes to its policies on intellectual property protections, technology transfers, industrial subsidies and domestic market access, along with steps to reduce a $375 billion U.S. goods trade deficit with China. He also accused China of unfair commercial practices. He backed out on a deal congressional Democrats said they struck with Trump to provide legal status to young undocumented immigrants.
Trump has imposed penalty tariffs of up to 25 percent on $250 billion of Chinese goods in a dispute over Beijing's plans for state-led development of technology industries. "I think only they can break the logjam".
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