Mr Trump has asked key USA officials to begin drafting potential terms, according to the report.
"The two leaders agreed to strengthen economic exchanges", he said, though he gave no indication of whether they had made any progress on settling the trade dispute.
In a press briefing after taking the role, China's ambassador to the UN, Ma Zhaoxu, said his country would use the chance to stir debate on "strengthening multilateralism". 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.
In response, "Asian stock markets jumped Friday, reflecting investor relief about upcoming trade talks between China and the US, as well as the dollar's gains against a basket of major currencies including the yen", reports MarketWatch.
"They are maybe too complex to be solved in just one meeting", he said.
Trump had a "long and very good" telephone conversation with his Chinese counterpart on Thursday.
A Justice Department indictment targeted two companies based in China and Taiwan and three individuals, saying they conspired to steal trade secrets from USA semiconductor company Micron Technology Inc.
Stocks surged in Hong Kong and China on the report of constructive talks between Trump and Xi, while the offshore yuan jumped as much as 0.5 percent for the biggest two-day gain since August. The Chinese "want to make a deal", he declared, adding: "Lots of great things are going to happen over the next short period of time". And we're doing very well.
Trump said a deal with China would also be good for Beijing.
"He wants to do it", Trump said of Xi.
I spoke with President Xi (Jinping) yesterday.
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".
This air of optimism is providing some inspiration for investors to put risk back into their portfolios, which is why global stocks and emerging market assets are benefiting from such headlines. The US also sued to stop the companies from exporting any products created using the trade secrets to America.
The leaders of the world's two largest economies made the remarks after their first publicly disclosed telephone conversation in nearly six months.