With Mr Trump casting doubt on the benefits of global free trade, Mrs May sees the Chinese president, Xi Jinping, as a potential economic ally.
"I think one of the things that was interesting to people in Davos was the speech that President Xi gave and the comments he made about the importance of free trade around the world," she said.
For its part, China would value a reaffirmation of UK support following the sharp deterioration in US-China ties that have followed Mr Trump's election.
"China can potentially help the UK at a difficult time and the UK can also help China," said a Chinese official, who declined to be identified.
"We are just waiting to see what Mr Trump's real policies will be," said one Chinese official. "But our commitment to free trade will not change and the importance we attach to UK ties will remain high."
Beijing also wants more concrete assistance from the UK, particularly over a nuclear power deal for a Chinese company that the Chinese feel has become bogged down in uncertainty over the UK's bureaucratic and regulatory procedures.
Mrs May deploys the language of a "golden era" in China-British relations, but Beijing has cooled on a series of high-profile projects since the departure from the government of former chancellor George Osborne, a keen Sinophile.
Chinese observers blame the changing mood in Beijing to several factors, including uncertainties following Britain's vote to leave the EU and China's own domestic economic concerns.
Mrs May will travel to Philadelphia on Thursday to meet senior Republicans, holding their annual Congressional retreat, where she is expected to urge the GOP not to turn its back on world trade.
On Friday she will become the first foreign leader to meet President Trump in the White House. Mrs May has promised to hold "very frank" talks with the US president, including urging him to maintain US support for Nato and the EU.
"I expect trade will be discussed as a key lever in how we increase prosperity for the people of the UK and the US," Mrs May's spokeswoman said.
The prime minister said last week that although the UK could not sign a new trade deal with the US while it was a member of the EU, the two sides could look to dismantle barriers which are an impediment to trade.
Mrs May's spokeswoman said the prime minister would reaffirm Britain's commitment to a two-state solution in the Middle East, confirming that the UK had no plans to follow Mr Trump's proposal to relocate the US embassy to Israel to Jerusalem.
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