TAIPEI—Taiwan’s Foxconn Technology Group, which assembles Apple Inc.’s iPhones in China, is looking at seven states in the American heartland where it would invest $10 billion or more to manufacture flat-panel screens and related equipment.

“Over the years, manufacturing of consumer goods has shifted out of the U.S.,” Terry Gou, the chairman of the company formally known as Hon Hai Precision Industry Co., told reporters after the company’s annual shareholders meeting Thursday. “We will bring our advanced technology there to...