"I think we'll make a deal with China", Trump was quoted by The Hill as saying.
The Trump administration this year has already imposed tariffs on $250 billion in trade with China and is threatening to impose tariffs on all remaining imports from China, which last year were worth $505 billion. We're getting closer to something.
It comes ahead of a key meeting between Mr Trump and China's President Xi Jinping at the G20 summit this month.
The United States has 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.
Trump's posture toward China has been closely watched by investors, who are looking for the possibility of tensions cooling in their market-shaking trade war.
"I hope teams from both sides can implement the agreements achieved by the two countries' leaders", the spokesperson said.
President Trump has made very clear to China that they must change their "unfair" trade practices including theft of US intellectual property.
Asian markets then added to their gains after Bloomberg News reported that Trump has asked USA cabinet officials to draft a possible trade deal with China ahead of a planned meeting with Xi at the G20 leaders summit in Buenos Aires later this month.
"It is now clear what adjustments we should make and what we should adhere to", Lu said.
The G20 summit will take place from November 30 to December 1.
Reports earlier Friday said that President Trump had asked officials to prepare a draft of a trade agreement with the world's second largest economy, prompting the Dow to rise.
The Trump administration has been imposing tariffs on various countries, including China, claiming that the United States was "being treated unfairly in trade" and accusing Beijing of "stealing intellectual property".
These include outright cybertheft and forcing USA companies to hand over trade secrets as the price of admission to the Chinese market.
However, a senior Trump administration official on dismissed the report as untrue, a CNBC reporter said in a post on Twitter. On Thursday, the U.S. accused a Chinese SOE of conspiring to steal trade secrets of USA chip maker Micron Technology as part of a United States justice department crackdown against China in cases of suspected economic espionage.