The US levied tariffs of 10 percent on $200 billion of Chinese products in September, with the rate set to increase to 25 percent by the end of the year.
Mr Trump has asked key United States officials to begin drafting potential terms, according to the report.
"The economic teams of the two countries should strengthen contact, conduct consultations on issues of mutual concern, and push for a mutually acceptable solution to China-US economic and trade issues", Xi said.
Just after the upbeat readouts of the Trump-Xi call, the Justice Department announced the latest in a list of actions against what the Trump administration calls China's cheating through intellectual property theft, unfair corporate subsidies and rules hampering United States corporations in China.
Stock markets in China gained on Friday after US President Donald Trump said trade talks with Beijing were "moving along nicely".
Earlier on Thursday, Chinese Premier Li Keqiang told a group of visiting U.S. politicians that China and the United States could overcome their differences and get relations back on track if they worked together in a spirit of mutual respect.
Tai Hui at JPMorgan Asset Management said a stabilising trade relationship between USA and China and more stimulus from Beijing would be the key ingredients to revive market confidence in Asia.
On Wednesday, US Secretary of State Mike Pompeo said China was probably Washington's biggest long term security challenge and the United States was engaged in a "multi-pronged effort.to convince China to behave like a normal nation on commerce" and respect worldwide law.
In a phone call with U.S. President Donald Trump, Xi also said China would continue to play a constructive role in the process.
But Trump struck a more affable tone on Twitter after the phone call with Xi.
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.
"The West feels comfortable that some kind of trade deal will get done, and that Xi will support the private sector", said Andy Wester, senior investment analyst at Proficio Capital Partners.
Jacob Parker, vice president of China operations at the US-China Business Council in Beijing, said there were plenty of challenges that would require significant negotiations in advance of a meeting between Trump and Xi to ensure success. But Kudlow cautioned that Trump would "aggressively" pursue his agenda against China, if no deals were reached on intellectual property theft, cybersecurity and tariffs on commodities, among other issues.
"While we are still cautious over a full resolution of recent tensions in the medium term, resumption of dialogue between Washington and Beijing would be good enough to investors for now", he told Bloomberg.