Worries about the increased tariffs the two sides have imposed on each other's goods contributed to a dizzying bout of volatility in financial markets this week. The higher tariffs raise costs for companies in both countries, and economists say that if they remain in place indefinitely, they could depress economic growth.
A Xi-Trump meeting, if it happens, would take place during a summit of leaders of the Group of 20 biggest global economies in Argentina in late November.
"I don't think any decision has been made in regards to a meeting," Treasury Secretary Steven Mnuchin told reporters Saturday in Bali, Indonesia, where he's attending global finance meetings.
Still, Larry Kudlow, Trump's top economic adviser, said in Washington on Friday that preparations for the talks were under way.
"It looks like there will be a meeting in Buenos Aires at the G-20," Kudlow said in an interview with CNBC. "We are looking at it. The Chinese are looking at it. Preparations are being made. I can't say 100 percent certainty, but there is no question everybody is looking at it."
Kudlow said that so far, the administration viewed China's negotiating offers as "rather unsatisfactory" but that "maybe talks between the two heads of state will bear fruit."
Asked if China would need to make specific concessions for such a meeting to take place, Mnuchin said, "To the extent that we can make progress toward a meeting I would encourage that and that's something we're having discussions about, but for the moment there's no preconditions. The president will decide on that."
The trade feud has been fueled by U.S. accusations that China engages in cyber-theft and coerces foreign companies into handing over technology in return for access to the Chinese market, as well as by Trump's anger over China's trade surplus with the U.S. It is far from clear that the U.S. might be preparing to consider lifting penalty tariffs on about $250 billion of Chinese products.
Mnuchin repeated the Trump administration's determination to achieve a more balanced trading relationship that does not require foreign companies to form joint ventures to transfer technology to gain market access.
Lu Kang, a spokesman for China's Foreign Ministry, offered no specifics Friday but said, "I have also seen the relevant reports."
The Wall Street Journal and the Washington Post have cited officials as saying Trump has decided to proceed with a meeting with Xi.
Global indexes bounced back sharply Friday after their recent plunges, on word of the possible presidential meeting, along with strong Chinese export data. Japan's Nikkei 225 index gained 0.5 percent to 22,694.66 after a nearly 4 percent loss on Thursday.
Hong Kong's Hang Seng surged 2.1 percent to 25,801.49. The Shanghai Composite index advanced 0.9 percent to 2,606.91. Shares recovered in Taiwan and rose throughout Southeast Asia.
On Wall Street, the Dow Jones Industrial Average jumped 305 points, or 1.2 percent, in late-morning trading, and the Nasdaq composite surged 138 points, or 1.9 percent. Later, both stock indexes gave up much of their gains.
Friday's volatility followed a swoon over the previous two days that erased 1,300 points from the Dow and dragged the S&P 500 down more than 5 percent.
Reports that Mnuchin has advised against labeling China a currency manipulator - a status that could trigger penalties - were also seen as easing tensions. The Chinese currency has been falling in value against the dollar in recent months, raising concerns that Beijing is devaluing its currency to make Chinese goods more competitive against U.S. products.
In his comments in Bali, Mnuchin did not say what the forthcoming Treasury report, set to come out next week, will conclude about China's currency practices. In the past, Treasury has placed China on a watch-list but found that Beijing did not meet the threshold to be labeled a currency manipulator.
Mnuchin met Thursday with Yi Gang, head of China's central bank.
"I expressed my concerns about the weakness of the currency." Mnuchin said.
He said that in the discussions he had with the Chinese, they had made clear that they didn't see a further weakening of the Chinese yuan as being in their interests.
Concerns have been raised that China, the largest foreign holder of U.S. Treasurys, might start dumping its holdings as a way to pressure the United States in the trade dispute. But Mnuchin said this possibility didn't concern him because it would be contrary to Beijing's economic interests to start dumping its Treasury holdings.
"That would be very costly for them," Mnuchin said.
China's surplus with the United States widened to a record $34.1 billion in September as exports to the American market rose 13 percent from a year earlier to $46.7 billion, down slightly from August's 13.4 percent growth. Imports of American goods increased 9 percent to $12.6 billion, down from August's 11.1 percent growth.
Beijing's exports to the United States have at least temporarily defied forecasts they would weaken after being hit by punitive U.S. tariffs of up to 25 percent.
September marked the second straight record Chinese monthly trade surplus with the United States. Export numbers have been buoyed by producers rushing to fill orders before American tariffs rose. But they also benefit from "robust U.S. demand" and a weaker Chinese currency, which makes their goods cheaper abroad, Louis Kuijs of Oxford Economics said in a report.
The Chinese yuan has lost nearly 10 percent of its value against the dollar this year. That prompted suggestions Beijing might weaken the exchange rate to help exporters. But that might hurt China's economy by encouraging an outflow of capital. The central bank has tightened controls on currency trading to prevent further declines.
Crutsinger reported from Washington. Associated Press writers Joe McDonald in Beijing and Annabelle Liang in Singapore and Elaine Kurtenbach in Bali, Indonesia, contributed to this report.
Copyright 2019 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.