The event will be closely watched for any progress in the resolution of the bitter trade dispute between the world's two largest economies.
The U.S. president said Wednesday that he'd like to sit down and make a "fair deal" with China on trade that would eliminate the need for the massive tariffs he's put on the nation. "We talked about many subjects, with a heavy emphasis on Trade", Mr Trump tweeted.
"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.
The Trump administration has imposed tariffs on $250 billion worth of Chinese goods, and Trump has suggested that tariffs could be coming for all other Chinese imports, worth as much as $267 billion, not now subject to duties.
Washington introduced the duties in response to what it says are long-running, unfair trading practices by China, and Beijing has retaliated in kind.
The trade dispute has also forced the yuan to fall in value but on Friday it was stronger for the first time this week, also helped by Xi's pledge on Thursday of more support for private firms.
Mr Trump has asked key United States officials to begin drafting potential terms, according to the report.
The Chinese president was also quoted as saying that he was willing to meet Trump in Argentina during the G-20 summit.
Tai Hui at JPMorgan Asset Management said a stabilising trade relationship between United States and China and more stimulus from Beijing would be the key ingredients to revive market confidence in Asia.
Asian stocks rose sharply on Friday on hopes of a trade deal between the United States and China.
The two countries already have imposed tariffs on hundreds of billions of dollars of each other's goods and Trump has threatened to slap tariffs on the remainder of China's $500 billion-plus exports to the United States if the disputes can not be resolved.
President Trump has made very clear to China that they must change their "unfair" trade practices including theft of US intellectual property.
The United States has imposed tariffs on $250 billion worth of Chinese goods so far, while China has retaliated with $110 billion worth of tariffs on U.S. goods.
"We will see what happens at the G20 and with Liu's talks, but I am not optimistic that anything momentous will come out of this", Zimmerman said.
Tensions have increased in recent months with United States officials accusing China of meddling in the USA midterm elections, conducting cyber espionage and military aggression.
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