Liu and a delegation will met with U.S. Trade Representative Robert Lighthizer and Treasury Secretary Steve Mnuchin on Wednesday.
The Chinese delegation has proposed to the United States that Mr Trump meet Mr Xi in the tropical Chinese city of Hainan after his planned summit with North Korean leader Kim Jong Un in late February, the Wall Street Journal reported, citing people briefed on the matter.
USA and Chinese negotiators on Wednesday opened two days of high-level talks aimed at settling a trade war that has weakened both economies.
"Meetings are going well with good intent and spirit on both sides", Trump wrote. The sides planned to engage in 90 days of negotiations with a view to achieving needed structural changes in China that affect trade between the two countries.
Meanwhile, Mr Trump, a self-described "Tariff Man", rejected a previous proposal from Beijing to resolve the dispute with increased purchases of USA goods.
Dennis Wilder, a former top China analyst for the Central Intelligence Agency, said the Chinese are betting they can secure a better deal in direct leader-to-leader horsetrading. "No final deal will be made until my friend President Xi, and I, meet in the near future to discuss and agree on some of the long standing and more hard points", Trump said in another posting.
Trump, meanwhile, has seen his public approval ratings battered by the partial government shutdown and is said to worry about the tariff war's impact upon USA financial markets.
"We hear rumblings or rumors there are some offers (by the Chinese delegation to Washington) around IP (intellectual property) enforcement, around the other sensitive issues".
Chinese Vice Premier Liu He is scheduled to meet with Trump today as pivotal trade talks conclude in Washington.
Russia Vows To Defend Its Venezuelan Oil Assets
The US has imposed sanctions on Venezuela's state-owned oil firm PDVSA after the country's president refused to step down. Inclusion on this list is a powerful tool with the potential to curb trade in Venezuelan oil far beyond US borders.
People's Bank of China Governor Yi Gang declined comment on Chinese proposals as he left the delegation's hotel for the meetings in Eisenhower Executive Office Building, next to the White House.
In a sign that Beijing is serious about addressing USA complaints, Chinese lawmakers this week completed a second review of a new law that is aimed at protecting the IP of foreign investors and banning forced technology transfers.
While the administration says its prosecution of Huawei is not related to the trade talks, the case illustrates what authorities have described as a long-standing problem in China.
China's top economic official Vice Premier Liu He is part of the delegation in the U.S. January 30 and 31.
Beijing hit back with duties on virtually every product it buys from the United States, about $110 billion in goods annually.
The administration has already imposed tariffs on some $250 billion in Chinese imports. Both sides agreed to start talks on reforms with respect to forced technology transfer, intellectual property protection, non-tariff barriers, cyber intrusions and cyber theft, and opening the Chinese market to US services and agriculture.
But the Chinese side would likely have to bring to the table a new offer that goes significantly beyond its previous offers to significantly increase purchases of US goods, including soybeans, energy and manufactured goods.
Last week, US Commerce Secretary Wilbur Ross said the two sides remained "miles and miles" apart.