In addition to the USA, the European Union, Japan, Germany and Canada have all expressed concern about China's behaviour on IP theft.
While China joined in a unanimous U.N. Security Council decision to tighten economic sanctions on Pyongyang over its long-range missile tests, it is not clear whether Trump thinks Beijing is doing enough.
The administration has been eyeing other moves to rebalance the U.S.
Mr Trump had been expected to order a so-called Section 301 investigation under the 1974 Trade Act earlier this month, but action had been postponed as the White House pressed for China's cooperation in reining in North Korea's nuclear programme.
"The [U.S. -China] relationship could spiral out of control, particularly if the movement on the trade front is combined with growing tensions over how to respond to North Korea", said Scott Kennedy, a China expert at the Center for Strategic and International Studies.
In a phone call Friday, Trump praised Chinese President Xi Jinping for backing the recent United Nations vote to impose tougher sanctions on North Korea, and the leaders reaffirmed their commitment to a nuclear-free Korean Peninsula.
Michael Wessel, a commissioner on the U.S.
Global tensions have escalated as Trump and North Korean President Kim Jung Un traded threats of nuclear war in recent days.
Trump wants government officials to look at Chinese practices that force American companies to share their intellectual property in order to gain access to the world's second largest economy.
Section 301 allows the president to impose tariffs on foreign products in response to unfair or discriminatory restrictions on American commerce.
Like the president, Lighthizer has criticized multilateral venues like the World Trade Organization for failing to provide adequate tools to address China's economic violations.
According to a third senior administration official, these investigations could take as much as a year before the US Trade Representative could come out with its determination.
Earlier this year, an independent commission on US intellectual property estimated that the annual cost to the USA economy in counterfeit goods, pirated software, and theft of trade secrets from all sources exceeds $225 billion and could be as high as $600 billion.
It may also prove to be a source of leverage to push China to do more to help contain a rising security threat from North Korea, which counts Beijing as its only powerful ally.
Trump, who is on a working vacation at his New Jersey golf club, said Friday that he planned to be in Washington on Monday "for a very important meeting" and "we're going to have a pretty big press conference".
USTR argues Beijing uses a range of practices to force USA companies to transfer IP, such as by granting regulatory approvals to drug makers that shift production to China or requiring that the designs of foreign products be replicable in China.
"I think China can do a lot more", Trump told reporters Thursday.
A 2013 report by a commission co-chaired by Jon Huntsman, ambassador to China under President Barack Obama and Trump's nominee to be Russian envoy, pegged the losses from United States intellectual property theft at hundreds of billions of dollars annually that cost the USA economy millions of jobs. They know how I feel.
The trade investigation could strain relations between the USA and China as the two countries wrestle with the unpredictable situation over North Korea.