The much-delayed offering, a cornerstone of de facto ruler Prince Mohammed's ambitious plan to diversify the oil-reliant economy, could exceed the world's biggest listing - the $25 billion float of Chinese retail giant Alibaba in 2014.
Aramco had initially been expected to list on two exchanges, with a first flotation of two percent on the kingdom's Tadawul bourse, followed by a further three percent on an overseas exchange.
But the firm has said there are no current plans for an international stock sale and the IPO seems to be banking on local demand, with one-third of the offering reserved for Saudi retail investors.
Aramco kicks off its investor road show on Sunday, but a source close to the company told AFP it will not be marketing the IPO overseas.
The source did not offer an explanation but the company has shied away from plans to list on foreign exchanges such as New York owing to litigation risks.
The launch has been dogged by delays since the idea was first announced in 2016, with Prince Mohammed's desired valuation of $2 trillion meeting with scepticism from investors and analysts.
"(The) first impression is that (the) price is a sensible compromise and that it will sell," Tarek Fadlallah, chief executive officer of the Middle East unit of Nomura Asset Management, said on Twitter.
If priced at the top end of the range, it could eclipse Alibaba to become the world's biggest IPO, Fadlallah added.
Saudi Arabia is pulling out all the stops to ensure the success of the IPO, a crucial part of Prince Mohammed's plan to wean the economy away from oil by pumping funds into megaprojects and non-energy industries.
"If subsequently effectively deployed, the funds raised could be used to support longer-term economic growth in Saudi Arabia," said S&P Global Ratings.
"We understand that the bulk of the funds raised will go to the government or the Public Investment Fund."
The government has reportedly pressed wealthy Saudi business families and institutions to invest, and many nationalists have labelled it a patriotic duty.
Among those considering a sizeable investment is Prince Al-Waleed bin Talal, a billionaire tycoon who was held in Riyadh's palatial Ritz-Carlton hotel in 2017 during a crackdown on corruption, Bloomberg News reported.
Last week senior cleric Abdullah al-Mutlaq sought to drum up support for the IPO among ordinary Saudis, saying in a local television programme that it was permissible in Islam and even religious scholars were likely to participate.
Even for the domestic listing though, there are reports the firm is struggling to attract foreign institutional investors, amid an uncertain outlook for the energy sector and questions over company disclosures and governance.
In its prospectus released last week, the company listed a variety of risks ranging from the possibility of anti-trust legislation to terrorist attacks and geopolitical tensions in a region dominated by Saudi-Iran rivalry.
One striking element was a warning that global oil demand may peak within the next 20 years, citing a forecast from industry consultant IHS Markit.
It also acknowledged that climate change concerns could reduce demand for hydrocarbons.
But Aramco, a cash cow that catapulted the kingdom to become the Arab world's biggest economy, does appear to hold enormous appeal for local retail investors.
Many Saudis are seeking to tap lenders and sell personal assets to raise money to invest in the share sale. Aramco last year posted $111.1 billion in net profit. In the first nine months of this year, its net profit dropped 18 percent compared with the corresponding period of 2018, to $68.2 billion.