The state-owned oil giant will determine the IPO launch price after registering interest from investors.
Business sources say the Saudis are expected to make shares available for 1% or 2% of the firm, and the offer will be for existing company shares.
Saudi Aramco is thought to be worth about $1.2tn (£927bn).
'Historic'
The firm said it has no current plans for a foreign share listing, saying long-discussed plans for a two-stage IPO including an offering on a foreign exchange had been put aside for now.
"For the (international) listing part, we will let you know in due course. So far it's only on Tadawul," Aramco chair Yasir al-Rumayyan told a media conference, referring to the Saudi stock exchange.
Chris Beauchamp, chief market analyst at derivatives traders IG Group, said: "Investing in Aramco carries risks, of course, and not only that oil prices will struggle to move higher.
"Political and strategic risks are high for any firm operating in the region, not least one which is an arm of the Saudi state. Aramco also has limited control in output policy, a key part of Saudi Arabia's Opec management."
Those potential risks were highlighted in September when drone attacks hit the Abqaiq oil facility and the Khurais oil field in Saudi Arabia, both owned by Aramco.
But Aramco boss Amin Nasser, who called the plans "historic", told a media conference after the IPO statement was published that the firm was still the most reliable oil company globally.
In its launch announcement Aramco said: "The company does not expect the impact of these attacks to have a material impact on its business, financial condition or results of operations."
