"The amounts of oil are incredible, and I have to rub my eyes frequently and say like the farmer: 'There ain't no such beast.' " So wrote an American oilman in the Persian Gulf a few years after the discovery in 1938 of a gusher of oil from Saudi Arabia's Well Number Seven, 4,727 feet below the desert floor.

You could say the same today about Saudi Aramco, the state-owned firm that for decades has had exclusive control of Saudi Arabia's oil and is the world's biggest, most coveted and secretive oil company. On Jan. 4, the kingdom's deputy crown prince, Muhammad bin Salman, told The Economist that Saudi Arabia was considering the possibility of floating shares in the company, and said he personally was "enthusiastic" about the idea.

It was a stunning revelation.

Officials say options under preliminary consideration range from listing some of Aramco's petrochemical and other "downstream" firms, to selling shares in the parent company, which includes the core business of producing crude. The staggered nationalization of the Arabian American Oil Company (Aramco), made up of four big American firms, in the 1970s was emblematic of a wave of "resource nationalism" that has helped define the industry.

Worth 'trillions of dollars'

Aramco is worth, officials say, "trillions of dollars," making it easily the world's biggest company. It says it has hydrocarbon reserves of 261 billion barrels, more than 10 times those of ExxonMobil, the largest private oil firm, which is worth $323 billion. It pumps more oil than the whole of the United States, about 10.2 million barrels a day, giving it unparalleled sway over prices. If just a sliver of its shares were placed on the Saudi stock exchange, which has a current total market value of about $400 billion, they could greatly increase its size.

Prince Muhammad says a listing would not only help the stock market, which opened to foreigners last year. It would also make Aramco more transparent and "counter corruption, if any."

A final decision has yet to be made. Yet the prince has held two recent meetings with senior Saudi officials, and diplomats say investors are being sounded out. The talk is of at first floating a small portion of the company in Riyadh, perhaps 5 percent. In time that could rise — though not by enough to jeopardize the kingdom's control of decisionmaking.

The aim would be to foster greater shareholder involvement in Saudi Arabia; a senior official said there was no intention of surrendering control of Aramco or its oil resources to foreign firms. But it is part of a frenzy of reforms proposed by the prince that his government is rushing to keep pace with.

For many investors, a listing of Aramco, however partial, would be a prize even at today's low oil prices.

Tide of nationalism

By the standards of national oil monopolies, analysts say Aramco is well run. In the 1940s and '50s, when the American consortium recruited young Saudis, it was an "unlikely union of Bedouin Arabs and Texas oil men, a traditional Islamic autocracy allied with modern American capitalism," says Daniel Yergin in "The Prize."

Under American ownership, it built towns with schools, wiped out malaria and cholera, and helped farmers become entrepreneurs, officials recall, explaining why it was popular with Saudis.

It was a different story in Iran and elsewhere, where citizens grew sick of the colonial-era concessions taken by British and French firms, and a wave of nationalization began. The Saudis, having declared their first 25 percent stake in Aramco in 1973 indissoluble, were unable to resist the tide. Full nationalization of Aramco came in 1980. But an American business ethic survived. Just over a decade ago Matthew Simmons, an American banker, argued that Saudi wells were past their prime and that production would soon peak. Yet Aramco has increased output by more than 1 million barrels per day in the past five years, reaching record highs.

Questions hover

Questions surround the company, though. One observer says 87 percent of its output is oil; it needs to develop more gas to satisfy the country's needs for cleaner, cheaper power. Some argue that its reserves, which have barely budged since the late 1980s, are overstated.

The company does not report its revenue. Its fleet of eight jets, including four Boeing 737s, and a string of soccer stadiums suggest it is not run on purely commercial lines. It is the government's project manager of choice even for non-oil developments, and runs a hospital system for 360,000 people. A listing would require it to become more transparent.

But even with greater disclosure, minority shareholders may play second fiddle. The company is integral to the social fabric of Saudi Arabia and the survival of the ruling Al Saud dynasty, providing up to nine-tenths of government revenue. Cuts in its output have been a foreign-policy lever through which OPEC, the producers' cartel, has often sought to rescue oil prices.

Prince Muhammad's desire for reform fits a pattern that some consider reckless. Saudi Arabia has recently forced OPEC to maintain production despite oil falling from a peak of $120 a barrel to below $35. Its decision on Jan. 3 to suspend diplomatic relations with Iran, a fellow OPEC member, makes it harder for both to agree on production cuts, though Saudi officials are adamant that they have no intention of rescuing prices.

Others believe Saudi Arabia's strategy makes sense. They think it wants to protect its share of the global oil market by driving high-cost producers to the wall at a time when unconventional forms of oil, such as American shale, have had gushing success. Another threat is alternative forms of energy, such as wind and solar, which may well challenge fossil fuels. Selling shares in Saudi Aramco could thus be intended to cash in before the "decarbonization" of the economy starts to gain credibility.

Copyright 2013 The Economist Newspaper Limited, London. All Rights Reserved. Reprinted with permission.