Iran, a Shiite Muslim state, and the United States have not had diplomatic ties since the 1979 storming of the American embassy in Tehran and the 444-day hostage crisis.
But there has been a growing recognition that Iran still dubbed by Washington a state sponsor of terrorism could play a role in helping to restore stability in countries such as Iraq and Syria.
Refusing to deny or confirm the report, White House spokesman Josh Earnest said "I'm not in a position to discuss private correspondence between the president and any world leader."
Iran and the United States are currently negotiating a complex deal to rein in Iranian nuclear ambitions in exchange for an easing of crippling international sanctions against the Islamic republic.
Earnest repeated that on the sidelines of those talks, being led by a group of powers known as the P5+1, Iran and US had discussed the threat of the militants.
But he reiterated US stand that "the United States will not cooperate militarily with Iran in that effort, we won't share intelligence with them."
In his letter, Obama reportedly stressed to Khamenei that any cooperation in fighting IS militants would depend on reaching a comprehensive nuclear deal, as a November 24 deadline looms.
US Secretary of State John Kerry will on Sunday meet with Iranian Foreign Minister Mohammad Javad Zarif as well as EU foreign policy chief Cathy Ashton in Oman, for a fresh round of nuclear talks.
They will meet in Muscat, which hosted secret Iran-US talks in 2012, widely credited for bringing Tehran back to the nuclear negotiations.

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