According to Reuters news reports, the official said both the sides could agree over common ground and not to impose further tariffs as a goodwill gesture in order to get negotiations resumed, but it was not clear whether that would happen.
Trump advisers have said no trade deal is expected at the meeting but they hope to create a path forward for talks.
Trump and Xi will sit down together at the Group of 20 summit meeting in Osaka, the first time they have done so since trade talks between the world's two largest economies broke down in May.
Speaking on the condition of anonymity, the official said Washington was unwilling to hold a meeting with Xi with any concessions. "We want him to stop funding coal and not to make climate change worse".
However, last week in D.C., Trump vowed that "anything I can do to help Canada I will be doing", in regard to the two Canadians being imprisoned in China ahead of a possible meeting with Chinese President Xi Jinping. Trump could also threaten to raise tariffs to 40 percent if talks fail, he warned, adding: "It's not going to solve the immediate problems".
In addition, each of the two leaders separately said their countries should champion "free trade", remarks that could be interpreted as veiled criticism of the United States.
The president began his battery of meetings with world leaders with a dinner with Australian Prime Minister Scott Morrison Thursday evening. "As we work jointly with Japan to tackle complex global challenges, I am continuously reminded of the pivotal importance of our alliance that is global in scope", Bolton tweeted later in the day.
FedEx sues United States government on task of overseeing China exports
Smith said the company remained committed to operating in China and "completely dedicated" to complying with Chinese laws. It looks like FedEx may now be going above and beyond even the Trump administration to enforce that ban on its own.
Ahead of the meeting, Trump has threatened to implement more tariffs on another round of Chinese goods, worth $300bn, including on everyday products used by USA consumers like electronics.
While prospects for detente in the trade war between the US and China are in the spotlight, many participating are calling for a broader perspective in tackling global crises. "So I hope the media also pays attention to the other aspects that will be discussed at the G20", pleaded Masatsugu Asakawa, Japan's top finance diplomat.
Meanwhile, Russian Deputy Foreign Minister Sergei Ryabkov also said that Moscow assumes that a Trump-Putin will likely take place at the upcoming G20 summit set for 28-29 June.
Since President Trump entered the White House in January 2017 the United States has refused to endorse langauge backed by the rest of the G20, backing the Paris Agreement and emphasising the need for ambitious action to curtail climate change.
"We should not just sit back and passively await our fate in the wake of a major power contest", the prime minister will tell the event.
Some experts say Trump and Xi could announce a cease-fire of sorts on the new tariffs and detail the resumption trade talks.