NEW DELHI—Apple Inc. is nearing a deal to manufacture its products in India, according to a senior government official, as the company seeks to boost its sales in a market that is home to more than 1.2 billion people.

A team of executives led by Priya Balasubramaniam, an Apple vice president, met with senior Indian government officials in New Delhi on Wednesday to discuss the firm’s proposals, the official said.

“It’s...