The Trump administration views these purchases as necessary to bolster the president’s support across farming and manufacturing communities hard hit by the trade war and to help narrow the gap between what China sells to the United States and what it buys. The administration has been working on various draft lists of what it wants China to purchase, according to people who have viewed them.

The final purchasing amount is not yet clear. In December, Mr. Mnuchin said that China had made an offer to buy more than $1.2 trillion in American goods as part of the talks. But economists and China analysts have cautioned that such a large amount could be hard for the United States to produce and export.

The United States exported just $120 billion of goods to China last year. With the American economy hovering near full employment, it lacks the productive capacity to raise exports by hundreds of billions of dollars in the short term. The United States could redirect some of the goods it sells to other countries to China instead, for instance diverting soybeans headed to Europe to China.

But a deal that would require China to buy even more from the United States is raising concerns that China could expand its leverage over the United States.

“If it can be negotiated by government fiat, it can be taken away by government fiat,” said Kevin Book, managing director at ClearView Energy Partners, an energy-focused research firm.

The deal could usher in a wave of new American exports if China agrees to open its markets more fully. Removing its requirements that American carmakers and financial services firms team up with a Chinese entity to do business in the country, for instance, could give those firms more ability to sell goods and services to China.

But in other industries, including agriculture, energy and aviation, purchases associated with a trade deal would be made directly by state-controlled entities. And while that would mean greater revenues for American companies, skeptics say it could also increase the leverage that China has over the United States in the future.