WASHINGTON—The Trump administration is seeking to blunt domestic opposition to its trade policies with a relief package for farmers affected by the U.S. trade spat with China, say officials involved in the discussions.

The aid package, which could climb into the billions of dollars, is still being developed. Agriculture and congressional officials are examining Depression-era programs like the Commodity Credit Corp., which was created in 1933 to stabilize farm incomes, and which permits borrowing of as much as $30 billion...