The report, quoting unnamed officials, said Iran had agreed to the talks for the first time but would not hold them until after US elections on 6 November.
The White House said it was prepared to meet Iran bilaterally, but that there was no plan to do so.
Western states think Iran is seeking nuclear weapons, something it denies.
Iran has been a key foreign policy topic in the US election campaign.
President Barack Obama and Republican challenger Mitt Romney will hold their third and final campaign debate on Monday, on the subject of foreign policy.
The New York Times report said the US and Iran had agreed to one-on-one negotiations “in principle”.
But US National Security Council spokesman Tommy Vietor said in a statement that it was untrue the US and Iran had “agreed to one-on-one talks or any meeting after the American elections”.
“We continue to work… on a diplomatic solution and have said from the outset that we would be prepared to meet bilaterally,” he added.
Negotiations between Iran and the P5+1 negotiation group – which includes the UK, US, France, China, Russia and Germany – have stalled.
Western nations have used increasingly harsh sanctions in an effort to pressure Iran over its nuclear programme.
Mitt Romney has accused Barack Obama of being too soft on Iran.
Barack Obama opposes a near-term military strike by the US or Israel on Iran’s nuclear facilities, but says he is determined to stop Iran from building a nuclear bomb.
“The president has made clear that he will prevent Iran from getting a nuclear weapon, and we will do what we must to achieve that,” Tommy Vietor said.
“The onus is on the Iranians to do so, otherwise they will continue to face crippling sanctions and increased pressure.”
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