Relations between Iran and the US have become more confrontational since Trump's election and his May 2018 decision to withdraw from the nuclear deal and reimpose severe economic sanctions on the Islamic Republic.
It is not known if Trump knew about the request made to the Pentagon.
The report said the move came after a mortar attack launched by an Iran-linked group on the Baghdad diplomatic quarters home to the U.S. embassy in September.
John Bolton, the national security adviser, called a series of meetings after the attack - which one of Tehran's proxy militias in Iraq claimed responsibility for - and is believed to have asked the Pentagon to draw up options for bombing Iran.
While it is unclear if the proposals were eventually sent to the White House or if the president knew of the plans, Bolton's request anxious many in the Pentagon and the State Department concerned with the more hawkish approach toward Tehran. The decision to seek options striking Iran was prompted by an incident in September in which three mortars were fired into a diplomatic quarter in Baghdad, the newspaper said. No one was hurt by the shells, which landed in an open lot.
"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. "People were shocked. It was mind-boggling how cavalier they were about hitting Iran".
Before joining the Trump administration, Bolton argued repeatedly that the U.S. should attack Iran and had supported regime change in the country.
There's no doubt that we could do plenty of damage to Iran if we chose to strike.
In the same month, US Secretary of State Mike Pompeo also stated the US was willing to target Iran for the actions of its allies in Iraq.
That policy could change if Iran continues to threaten its neighbors in the region. The Iranians could do plenty of damage to us if they chose to retaliate.
Pompeo said on Friday that the summit, to be held in Warsaw on 13-14 February, would focus on stability and security in the Middle East, including on the "important element of making sure that Iran is not a destabilising influence".