Hopes have been raised and dashed several times over the last few years. While the Saudi government has long considered the reform and has been making technical preparations , it has never set a date for opening the market.
Authorities are believed to worry about destabilising the market with fresh inflows of funds. Also, letting foreigners buy more stocks could be politically sensitive, if the foreigners are perceived to be obtaining Saudi assets at bargain prices.
In the last few months, however, several events have convinced many people that the authorities are now preparing to finally open the market, possibly within months.
Partly in response to such hopes, the main Saudi stock index is up 21 percent year-to-date despite sluggish earnings growth for its two biggest sectors, banks and petrochemicals.
Some blue chips that could be expected to draw the interest of foreign institutional investors have picked up in the last few weeks. Saudi Basic Industries Corp (SABIC), the world's biggest petrochemicals producer, has jumped 6 percent over the past 10 trading days.
"An announcement is expected anytime between now and June 2014," said Mohammad Omran, president of Riyadh's Gulf Centre for Financial Consultancy, a private body. He is a member of the Riyadh Chamber of Commerce and Industry's investment and securities committee.
A Dubai-based fund manager, who asked not to be identified because of the commercial sensitivity of the issue, said: "Talk among top executives is that everything is in place and authorities are waiting for the final word from the king."
Saudi Arabia is the Arab world's biggest stock market by far and by some measures, the world's last sizeable market that has not opened to international capital flows.
Its $417 billion capitalisation in July dwarfed the Gulf's second market, Qatar, at about $110 billion; Saudi Arabia was smaller than Mexico at $508 billion but larger than Thailand at $399 billion, according to the World Federation of Exchanges.
Currently, foreigners - excluding Gulf Cooperation Council nationals, who have special access - can only buy Saudi shares through swap deals made by international investment banks or via a small number of exchange-traded funds.
These arrangements can be costly and inconvenient. Foreigners are believed to own no more than around 5 percent of the market; they accounted for 2.8 percent of stock trading turnover in July, according to exchange data.
Such figures  suggest an opening to direct investment could attract billions of dollars of additional inflows. Even a rise in foreign ownership to a moderate level of 15 percent of the market could mean fresh flows of about $40 billion over time.
Expectations for a market opening have strengthened since Mohammed bin Abdulmalik Al al-Sheikh was appointed head of the Capital Market Authority (CMA), the regulator, in February.
Al-Sheikh, a former World Bank executive, is seen as more comfortable than his predecessor with international markets; he said in May that the country was finalising a regulatory framework to let foreigners directly own stocks in the kingdom.
A set of new regulations has followed Al-Sheikh's appointment, an apparent effort to reduce the dominance of individual short-term speculators in the Saudi market and make it more welcoming to longer-term institutional investors such as foreign asset managers.
The CMA capped each stock's rise on its first day of trading at 10 percent, giving institutions more time to get into new issues. It proposed sanctioning listed firms if their accumulated losses exceeded 50 percent of their capital; the current regulation specifies 75 percent.
A new incentive to open up the market is international index compiler MSCI's decision in June to upgrade Qatar and the United Arab Emirates to emerging market status from next June, leaving Saudi behind. MSCI indexes are used as benchmarks by many global investment firms.
Access to foreign investment is a key criterion for inclusion in MSCI indexes and because of its restrictions, Saudi Arabia is not even in MSCI's frontier markets index. So it risks missing out as its neighbours attract increasing amounts of foreign cash.
"The MSCI upgrade for the UAE and Qatar is an incentive for the CMA to work hard and fulfill the requirements to make sure it is included in the emerging market index," Omran said.
Proposals circulated by authorities to the financial industry last year indicate Saudi Arabia will follow a model similar to China, Taiwan and some other major emerging markets in opening its bourse.
Qualified foreign investors, awarded licences based on factors such as the amount of their assets under management, would be given quotas for their investment in the market.
This would allow authorities to open the market gradually as licences are awarded, and to regulate the size of fund inflows in response to market conditions. While details of the Saudi framework do not appear to have been finalised, enough study has occurred for the framework to be introduced quickly.
Two other trends suggest to many market participants that an opening is near. One is Saudi efforts this year to restructure the economy and make it more efficient, by seeking, for example, to limit the use of foreign labour and push more Saudi citizens into the private sector.
Another reform was Saudi Arabia's switch in June to a Sunday-Thursday working week from Saturday-Wednesday; this aligned Saudi financial markets more closely with trading hours in the rest of the world, making foreign participation easier.
Bringing foreign investors into the stock market is seen as part of the economic reform drive because it would expose stock prices to disciplined long-term investors.
The market's rebound this year may also encourage authorities to open it up. Saudi Arabia's market is now well off multi-year lows hit in the wake  of its 2007-2009 crash and that will make it harder to argue that foreigners are getting a chance to buy stocks at unfairly low prices.