Trump's top economic adviser, Larry Kudlow, told CNBC Thursday that, "There's some movement toward" a meeting at the G-20.
China retaliated last month by putting tariffs ranging from 5 to 10 percent on $60 billion worth of American goods, coming into effect the same day as the American measures.
China's trade surplus with the United States hit a record $34.1 billion last month, according to official figures released in Beijing on Friday, news that is likely to further inflame the trade dispute with the United States.
Reports that U.S. Treasury Secretary Steven Mnuchin has advised against labeling China as a currency manipulator - a status that could trigger penalties - were also seen as easing tensions.
Julian Evans-Pritchard, an economist at Capital Economics, tells the Post that one reason that China has been able to beat Trump's tariffs so far is that its currency value has depreciated by more than eight percent since June, which has helped make its products even cheaper overseas, while also reducing domestic demand for US imports.
China's trade surplus with the USA grew 10 percent in September from a record $31bn in August, according to China's customs administration - a 22 percent jump from the same month a year ago.
Chinese exports to the United States have at least temporarily defied forecasts they would weaken after being hit by punitive USA tariffs of up to 25 percent. The Chinese are looking at it. Preparations are being made.
"Exports continued to defy USA tariffs last month but imports struggled in the face of cooling domestic demand", said Julian Evans-Pritchard of Capital Economics in a report.
The two countries imposed new tariffs on a massive amount of each other's goods mid-September, with the U.S. targeting $200 billion in Chinese imports and Beijing firing back at $60 billion worth of United States goods.
China's trade surplus with the USA in September was more than China's total trade surplus of US$31.7 billion.
He said although the Chinese want to negotiate, he does not believe they are ready.
For January-September, China's trade surplus with the United States was $225.79 billion, compared with about $196.01 billion in the same period a year ago.
The yuan has lost almost 10 percent of its value against the United States 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.
"China's trade surplus will keep rising because the domestic economy is cooling down", said Andy Xie, a Shanghai-based independent economist. The central bank has tightened controls on currency trading to head off further declines.