The proposal was prepared by Defense Secretary Jim Mattis, Secretary of State Rex Tillerson, National Security Adviser H.R. McMaster and other top officials, and presented to Trump at a National Security Council meeting on Friday, the sources told Reuters.
It could be agreed and made public before the end of September, two of the sources said. All of the sources are familiar with the draft and requested anonymity because Trump has yet to act on it.
The plan is intended to increase the pressure on Tehran to curb its ballistic missile programs and support for militants, the sources said.
"I would call it a broad strategy for the range of Iranian malign activities: Financial materials, support for terror, destabilization in the region, especially Syria and Iraq and Yemen," said one senior administration official.
The proposal also targets cyber espionage and other activity and potentially nuclear proliferation, the official said.
The administration is still debating a new stance on a 2015 agreement, sealed by President Barack Obama, Trump's predecessor, to curb Iran's nuclear weapons program. The draft urges consideration of tougher economic sanctions if Iran violates the 2015 agreement.
The proposal includes more aggressive US interceptions of Iranian arms shipments such as those to Houthi militias in Yemen and Palestinian groups in Gaza and Egypt's Sinai, a current official and a knowledgeable former US official said.
The plan also recommends the US react more aggressively in Bahrain, the sources said.
In addition, US naval forces could react more forcefully when harassed by armed speed boats operated by the Iran's Revolutionary Guard Corps (IRGC), Iran's paramilitary and espionage contingent, three of the sources said.
US ships have fired flares and warning shots to drive off IRGC boats that made what were viewed as threatening approaches after refusing to heed radio warnings in the passageway for 35 percent of the world's seaborne petroleum exports.
US commanders now are permitted to open fire only when they think their vessels and the lives of their crews are endangered. The sources offered no details of the proposed changes in the rules, which are classified.