Saudi Aramco is also negotiating with C.N.P.C., the Chinese state oil company, for the joint construction of a giant refinery in southwestern Yunnan province. It has investments in other refineries in Japan, China, South Korea and Indonesia.

The effort to focus more financial firepower on global refineries is also part of a larger strategy to diversify investments in areas other than drilling for crude oil on the Arabian Peninsula. A public offering of at least some refineries is being considered to bolster Saudi Aramco’s financial position, even as the company is making a concerted effort to expand production of refined products, including gasoline and diesel.

The Lyondell refinery, one of the largest in the United States, is designed to process low-quality, high sulfur crude oil. In recent years it has mostly processed Mexican crude and Canadian heavy oil from oil sands, but it could just as easily process low grade Saudi crude that refineries in Europe and Asia are not designed to refine.

United States refineries get a competitive edge on world markets from the low costs of American natural gas that produces power for the plants.

The possible purchase of the Lyondell refinery comes at a time when Saudi Aramco and Shell are going their separate ways, ahead of the planned disbanding of their Motiva joint venture early next year. The two companies are still working out the details, but Saudi Aramco is poised to gain complete control over the Port Arthur refinery as well as a chain of gasoline stations and storage facilities, while Shell will take over two smaller refineries in Louisiana — Convent and Norco — that were jointly owned.

Middle East oil experts say the impending loss of a piece of those two refineries would make the acquisition of Lyondell refinery all the more essential to maintain Saudi Aramco’s dominant market position along the Gulf of Mexico coast.

“Aramco has a keen interest in maintaining its downstream market share in the U.S.,” said Sadad I. al-Husseini, a former Saudi Aramco executive vice president. “The Lyondell refinery, because of its size and location will go a long way towards sustaining this strategy after the breakup of Motiva and the loss of the Convent and Norco refineries.”