The US president spoke to Xi on Thursday and later tweeted that trade talks with China were "moving along nicely" ahead of face-to-face talks between the pair at the G20 summit in Argentina later this month.
Stock markets in China gained on Friday after US President Donald Trump said trade talks with Beijing were "moving along nicely".
Trump said he and Xi also had "a good discussion on North Korea".
"Just had a long and very good conversation with President Xi Jinping of China".
Trump made no mention of whether the two leaders talked about the US indictment unveiled Thursday of two companies based in China and Taiwan accusing them of stealing trade secrets from a USA semiconductor company, Micron Technology Inc.
Though final decisions have not been made, USA officials are preparing for such a scenario in case a planned Trump-Xi meeting yields no progress on the sidelines of a Group of 20 summit in Buenos Aires in November, according to the report.
Trump revealed Thursday that he had spoken with Xi on several subjects, but focused on trade.
The possible warming of relations comes after months of escalating tensions over trade that are threatening to spill into other areas of disagreement, including freedom of navigation in the South China Sea.
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"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-U.S. trade issue, ' Xi said. "China would love to make a deal", Trump told Breitbart at the time.
The moves also follow media reports that pointed to progress on the US-China trade dispute.
U.S. Attorney General Jeff Sessions told reporters that Chinese espionage has been "increasing rapidly", demanding that "cheating must stop".
China's Premier Li Keqiang, right, speaks next to Tennessee Senator Lamar Alexander during a meeting with a group of U.S. Republican senators and Congress members at Zhongnanhai leadership compound in Beijing, Thursday, Nov. 1, 2018.
'We're going way up, and China has been hurt over the last number of months.
Trump administration officials have said that trade talks with China can not resume until Beijing comes up with specific actions it is willing take to meet USA demands for sweeping changes to policies on technology transfers, industrial subsidies and market access.
One person said a sticking point in any potential deal is intellectual property theft, where the Trump administration has sought to take a hard line.