According to The Wall Street Journal and Axios, Vance sent a letter to Mohsen Rezaei, secretary of Iran's Supreme National Security Council and a former commander of the Islamic Revolutionary Guard Corps.
The letter explored reopening negotiations between Washington and Tehran.
A U.S. official told Axios that any renewed talks would need to address Iran's nuclear program.
Trump acknowledged approving the outreach but publicly described the communication as an effort to facilitate medical supplies.
The diplomatic initiative comes amid reports that the United States has warned Gulf allies to prepare for possible renewed military operations against Iran after the November 3 elections.
The central disagreement remains unresolved.
Washington wants Iran to negotiate over its nuclear program before receiving economic relief.
Tehran wants the U.S. naval blockade lifted, frozen funds released, and restrictions on oil exports eased.
No comprehensive peace agreement has been reached, and no final decision on renewed U.S. strikes has been confirmed.
The bottom line: The Trump administration is pursuing diplomacy while keeping military options available. For investors, the next major development will be whether Tehran formally agrees to renewed negotiations. A credible agreement could reduce oil's geopolitical risk premium, while renewed fighting could further disrupt global energy supplies.