That's according to The Wall Street Journal's Benoit Faucon, who cited Ibrahim Muhanna, an oil ministry adviser, speaking at a conference in Paris.
The listed shares could amount to $125 billion in value, according to the report.
Muhanna also said the government is considering holding the offering on a New York, London, or Hong Kong exchange, in addition to Saudi Arabia's Tadawul, according to the report.
On Tuesday, Bloomberg reported that JPMorgan and the boutique bank M. Klein & Co. are advising on the potential offering.
The fact that Saudi Arabia was considering selling shares of Aramco came as a surprise to bankers. It was revealed in an Economist interview with Saudi Arabia's deputy crown prince, Muhammad bin Salman, in January.
Of course, there's still a chance the deal will not go through. The Saudi government is still reportedly in early-stage talks, and has not made any final decisions on the deal. Not to mention the fact that oil is hovering around its lowest prices in decades.