"And let's see what happens", Trump said at a White House event.
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.
Trump, in a tweet after their discussion, said he planned for the two leaders to meet at the G20 summit in Argentina later this month.
"We're doing a normal, routine run-through of things that we've already put together and normal preparation", he said.
Asian stocks rose sharply on Friday on hopes of a trade deal between the United States and China.
In their May telephone conversation, Xi and Trump set out to resolve their trade disputes, but the talks ended in stalemate and the first tariffs followed just weeks later.
The US and China's tit-for-tat tariffs on each other's goods have rumbled on for months as Trump pledges to help create more US manufacturing jobs. "We talked about many subjects, with a heavy emphasis on Trade", he wrote. America's trade deficit with China hit a record high in September, according to figures reported Friday by the U.S. Commerce Department.
Washington introduced the duties in response to what it says are long-running, unfair trading practices by China, and Beijing has retaliated in kind. "Rebuilt China", Trump told Breitbart at the time.
Alec Baldwin arrested in alleged parking dispute punch
Baldwin, 60, lives in the downtown Manhattan neighborhood with his wife, Hilaria Baldwin, 34, and their four children. The department said that Baldwin would "likely" be charged with misdemeanor assault.
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.
"He wants to do it", Trump said of Xi. "But China very much wants to make a deal", he said.
President Trump has made very clear to China that they must change their "unfair" trade practices including theft of US intellectual property. "Those discussions are moving along nicely with meetings being scheduled at the G-20 in Argentina".
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.
Washington accuses the two companies of stealing trade secrets from United States memory chip maker Micron Technology, but China's commerce ministry opposes the charges and has demanded Washington "remedy the mistake".
China and the United States can overcome their differences and get relations back on track if they work together in a spirit of mutual respect, Chinese Premier Li Keqiang told a group of visiting US politicians on Thursday.
Trump's posture toward China has been closely watched by investors, who are looking for the possibility of tensions cooling.