The initial public offering of Saudi Arabia's state oil giant's shares will take place over two stages: A flotation on the Saudi stock exchange later this year, followed by an international listing in 2020 or 2021, the Journal reported, citing advisors and officials familiar with the plans.
Aramco's IPO, when it goes ahead, is expected to be the world's largest.
The company had targeted to raise $100 billion through selling 5% of its share in the public markets, but it's not clear what the final amount will be, according to the report.
Many stock exchanges around the world have courted Aramco to list on their markets, with London and Hong Kong widely considered the front-runners to clinch the deal. But political uncertainties facing the two cities — arising from Brexit, the U.K.'s impending departure from the European Union, as well as prolonged protests in Hong Kong — have diminished their attractiveness, the report said.
Still, Saudi officials and Aramco advisors told the Journal that while they're leaning toward picking Tokyo, no final decision has been made and all options were still on the table.
In response to CNBC's request for comment, Aramco said it "continues to engage with the shareholder on IPO readiness activities." The company added it "is ready and timing will depend on market conditions and be at a time of the shareholder's choosing."
A spokesman from Japan Exchange Group, which runs the Tokyo Stock Exchange, told CNBC the firm has not changed its stance of wanting Aramco to list on its market.