However, a senior Trump administration reportedly denied that Trump was preparing to make a deal, a CNBC journalist said in a Twitter post on Friday.
Tensions have increased in recent months with USA officials accusing China of meddling in the U.S. midterm elections, conducting cyber espionage and military aggression.
Trump imposed new tariffs on roughly half of Chinese imports this summer, while Beijing fired back with tariffs on most USA products.
The moves also follow media reports that pointed to progress on the US-China trade dispute. It was the fourth such case since September alleging Chinese espionage on USA economic interests.
"Positive comments from President Trump over US-China trade tension are cheering the market in the short term", said Tai Hui, chief market strategist for Asia Pacific at JP Morgan Asset Management.
Trump and Xi, in several reciprocal actions, have in recent months imposed higher tariffs on tens of billions of dollars of exports moving between the two countries, increasing tensions between Washington and Beijing.
China and the US, the world's two largest economies, are in a bitter trade dispute.
Xi was quoted by CCTV as saying after the call with Trump that the two leaders had hoped to expand trade cooperation.
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The two countries have been locked in an escalating trade war this year, with each side imposing tariffs on hundreds of billions of dollars' worth of imports from the other.
Tu Xinquan, a trade expert at Beijing's University of International Business and Economics, said he was skeptical that the Trump administration was truly ready to deal, and that other factors, such as the mid-term congressional elections, could be driving statements from the administration.
Kudlow believes China is getting isolated in the ongoing trade war, as the United States, Japan, and the European Union officials met in September in NY on the sidelines of the U.N. General Assembly and reached a deal to tackle China's unfair trade practices.
Despite the positive message from Beijing, analysts were more pragmatic about what could be achieved by the leaders' meeting given the two sides' huge differences on strategic and ideological issues, as well as the growing hostility towards China in the United States.
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.
Xinhua, China's state news agency, reported on Friday that Mr Trump had told the Chinese leader that "he looks forward to meeting Xi during the G-20 summit so they can have an in-depth discussion about some major issues".
The US this year has already imposed tariffs on US$250 billion in trade with China.
China has responded with retaliatory duties on $110-billion worth of USA goods.