NEW DELHI—Apple Inc. is discussing with the Indian government the possibility of manufacturing its products in the country, according to two senior government officials, as the company seeks to expand its sales and presence in the South Asian nation.

In a letter to the government last month, the Cupertino, Calif., firm outlined its plans and sought financial incentives to move ahead, the officials told The Wall Street Journal. Senior Trade Ministry authorities in recent weeks met to discuss the matter.

An...