Both Trump and Chinese President Xi Jinping are due to attend the G20 summit in Argentina which starts at the end of this month, and could hold talks there.
In a phone call with U.S. President Donald Trump, Xi also said China would continue to play a constructive role in the process.
"President Xi Jinping also stressed that China-U.S. trade has always been serving as ballast and a stabilizer for China-U.S. relations". "Those discussions are moving along nicely with meetings being scheduled at the G-20 in Argentina".
Xi was quoted as saying after the call with Trump that they had hoped to expand trade cooperation. 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. The U.S.is preparing to announce tariffs on all remaining Chinese imports by early December should talks between the two powers fail to ease the trade war, Bloomberg reported last month.
China and the United States are locked in an increasingly bitter trade war, with both countries have already placed tariffs on some of each others imports.
Separately, the South China Morning Post - also citing unnamed sources - reported that Mr Trump had offered to host a dinner for the Chinese president after the G20 summit.More news: Khashoggi was strangled and dismembered - but fate of body still a mystery
Although U.S. -China relations have been rocky, Keqiang said he is optimistic both nations can work together in the spirit of mutual respect.
Meeting a group of Republican lawmakers in Beijing, China's Li noted the China-US relationship's "ups and downs" over the past four decades of diplomatic ties.
Tennessee Senator Lamar Alexander told Li that the delegation was there "to show our respect to a great country and a great people".
The rally in China-related stocks comes after a months-long slump, which has seen MCHI decline almost 17 percent since the beginning of the year and FXI fall more than 11 percent.
"China wants to make a deal".
The United States has already imposed tariffs on $250 billion worth of Chinese goods, with duties on $200 billion of the total set to increase to 25 percent from 10 percent on January 1, 2019. And they're having a hard time, and they'll be fine. I think we have a long way to go.