The Al-Eqtisadiah daily quoted an unnamed official as saying the sale would raise funds to be spent "at home and abroad" in what is expected to form the world's largest state investment fund.
The kingdom is looking to diversify its oil-dependent economy and has already announced cutbacks after its 2015 deficit snowballed to USD 97 billion (93 billion euros).
The IPO for state-owned Aramco could take place in 2018 and an initial sale of a five percent share is expected to form the basis for the fund holding around USD 2 trillion in assets.
Riyadh earlier this month agreed to slash its oil production beyond cuts agreed among OPEC members, giving crude prices a lift. They remain at around half of their mid-2014 levels.