The outgoing president made the request in the Oval Office last Thursday but was talked out of it by senior administration officials, according to the New York Times.
Mr Trump was reportedly told by vice president Mike Pence, secretary of state Mike Pompeo and others that such action could lead to a wider escalation of conflict in the final weeks of his presidency.
“A range of senior advisers dissuaded the president from moving ahead with a military strike,” reported the Times.
The subject was apparently raised after international inspectors reported a large increase in Iran’s stockpile of nuclear material.
The International Atomic Energy Agency reported last Wednesday that Iran’s uranium stockpile at Natanz was now 12 times larger than allowed under the nuclear agreement Mr Trump shelved in 2018.
Mr Trump asked his national security advisors what options he had to respond, according to the paper.
After the president was told of the risks that accompanied military action, officials “left the meeting believing a missile attack inside Iran was off the table," reported the Times.
Mr Trump might still take action against other Iranian assets or allies, said officials with knowledge of the meeting.
White House officials have not commented on the report.
Experts say that the stockpile of more than 5,385 pounds, of low-enriched uranium, would be enough to make two nuclear missiles.
But the material would require months of enriching to bring it up to bomb-making quality and Iran would reportedly not have weapons capability until next spring, after Mr Trump has left office.
Two years ago Mr Trump unilaterally pulled the US out of a 2015 international deal with Iran designed to slow its alleged efforts to build a nuclear weapon. During the election campaign this year, the president repeatedly claimed that should he be returned to the White House for a second term, the first call he would receive would be from Tehran, begging for a new deal.
Joe Biden vowed during the election campaign that he would re-enter the Iran nuclear deal if they agreed to again be limited by it.
But any military action towards Iran by Mr Trump in the final days of his presidency could increase the difficulty for the president-elect to revive the agreement with Tehran.