We are looking to upgrade this, and evaluate what type of products and facilities we need for the local market and beyond," Hariri said of the plant near the city of Basra.
Alexandra Wright, a spokeswoman for Shell in London, and a spokesman for Dow declined to comment.
U.S. State Department spokesman Tom Casey said the U.S. welcomed foreign investment in Iraq. "Part of the puzzle that needs to be solved and dealt with as Iraq continues to develop its political system, is to provide economic opportunity for the people there and to provide jobs," he said.
Iraq, which holds the world's third-largest oil reserves, produces most of its crude in the south of the country.
The nation pumped 2.07 million barrels per day last month, making it the Middle East's fifth-largest producer, according to a Reuters survey this month.