The New York Times reported Saturday that administration officials in Washington said the first-ever direct negotiations between the two countries were agreed to following what they called intense, secret exchanges.
National Security Council spokesman Tommy Vietor denied that such an agreement was made, but one administration official, speaking on condition of anonymity, said Iran has indicated it wants to discuss regional issues such as Syria with the United States.
Graham said he thinks "the time for talking is over" in an interview on "Fox News Sunday."
"I think the Iranians are trying to take advantage of our election cycle, to continue to talk. As we talk with the Iranians, whether it is bilaterally or unilaterally, they continue to enrich. And the vice president and the president said we will do nothing without coordinating with Israel. So we've talked with them in Moscow, we've talked with them in Baghdad, they continue to enrich, enrich," he said.
"We should be demanding transparency and access to the nuclear program. They doubled their centrifuges," he added. "So, I think this is a ploy by the Iranians."
Graham said he thinks it's clever of Iran to take advantage of the U.S. election cycle, and "I hope we don't take the bait."
Sen. Richard Durbin, D-Ill., said Iran's potential willingness to talk is a clear indication U.S. sanctions are working.
"This month of October, the currency in Iran has declined 40 percent in value. There is unrest in the streets of Tehran, and the leaders in Iran are feeling it. That's exactly what we wanted the sanctions program to do," he said.
"I think it's a clear indication, the sanctions regime that President Obama has put together with Israel and many nations around the world, is putting pressure on Iran to sit down and finally acknowledge that they cannot have a nuclear weapon. I think it is a positive step forward," he added.