The US blamed Tehran despite the Iranian administration denying the attack, which saw three mortar shells land in Baghdad's diplomatic quarter and close to the US Embassy last September. A second attack by an unknown group two days later targeted the USA consulate in Basra.
Asked about the report during his Middle East trip, US Secretary of State Mike Pompeo declined to comment.
But a direct air strike on Iran in response to a failed mortar attack that injured no one could easily trigger an all-out war across the region, and easily send chills down spines among Pentagon warplanners.
According to the paper, Mira Ricardel, the former deputy national security adviser, described the attack on the United States embassy in Iraq as "an act of war", and said that the USA needed to respond accordingly. The request generated concern at the Pentagon and State Department, current and former USA officials told the newspaper.
The Journal, citing conversations with people familiar with the request to the council, also reported that the council requested options for launching strikes at both Iraq and Syria when they made the request for Iran. It isn't clear whether the information compiled by the Pentagon was relayed to the White House or whether Trump was aware of the request, the newspaper said.
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As a think tank scholar and Fox News commentator, Bolton often urged Washington to attack Iran, including in a 2015 New York Times op-ed titled: "To stop Iran's bomb, bomb Iran".
The decision to abandon the Iran deal came one month after Bolton took over as national security adviser in April.
The US blamed Iran-aligned militants for the incident, although there were no immediate claims of responsibility for the attack.
"The Department of Defense is a planning organization and provides the president military options for a variety of threats", Colonel Rob Manning, a Pentagon spokesman, told AFP.
Washington withdrew from the Iran nuclear deal in May a year ago and re-imposed batches of sanctions on Tehran.