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Google parent Alphabet Inc
It is not clear specifically whose data the centres would house or who would control them, the WSJ said.
Reuters could not immediately reach Aramco and Alphabet for comment.
Alphabet rivals Apple Inc
A joint venture between Alphabet and Aramco could help Saudi Aramco expand into the United States, a goal for the oil company.
The size of the potential venture is unclear, although it could be big enough to become listed on Saudi Arabia's stock exchange, according to the Journal report.
It was unclear where Aramco would list its shares ahead of an initial public offering that could turn it into the world's largest publicly traded company.