The company has published an updated prospectus for its initial public offering (IPO), seeking more than $25bn for the sale of 1.5% of its shares.
That would make it potentially the world's biggest IPO, coming from the world's most profitable company
It is short of the $2tn valuation that Crown Prince Mohammed bin Salman was reportedly keen to achieve.
"The base offer size will be 1.5% of the company's outstanding shares," the state-owned energy giant said in a statement that set the price range at 30-32 Saudi riyals per share ($8-$8.5).
That could value the IPO at as much as 96bn riyals ($25.60bn) at the top end of the range.
If priced at the top end, the deal could just beat the record-breaking $25bn raised by Chinese e-commerce giant Alibaba in 2014.
Individual retail investors, as well as big institutions, will have a chance to buy shares.
Aramco had initially been expected to sell some 5% of its shares on two exchanges, with a first listing of 2% on the kingdom's Tadawul bourse, and then another 3% on an overseas exchange.
The firm says there are now no current plans for an international sale, with that long-discussed goal now seemingly being put on ice.
The crown prince is seeking to sell the shares to raise billions of dollars to diversify the Saudi economy away from oil by investing in non-energy industries.
Analysts S&P Global Ratings said the stock market debut could enable Saudi Arabia to strengthen its financial position.
"If subsequently effectively deployed, the funds raised could be used to support longer-term economic growth in Saudi Arabia," it said.
In its prospectus released last week, the company lists a variety of investment risks ranging from terrorist attacks to geopolitical tensions in a region dominated by Saudi-Iran rivalry.
The 600-page prospectus also includes the government's control over oil output as another potential risk.
After the flotation, Aramco will not list any more shares for six months, the prospectus says. Although one of the attractions for investors is the potential of high dividends, the document said Aramco has the right to change dividend policy without prior notice.
Aramco has hired a host of international banking giants including Citibank, Credit Suisse and HSBC as financial advisers to assess interest in the share sale and set a price. Based on the level of interest.
The sale of the company, first mooted four years ago, has been overshadowed by delays and criticism of corporate transparency at Saudi Arabia's crown jewel.
Aramco last year posted $111bn in net profit. In the first nine months of this year, its net profit dropped 18% to $68bn.