The presidents are both due to address the United Nations General Assembly on Tuesday, prompting speculation over whether or not the two will shake hands.
No American president has met a top Iranian leader since Shah Mohammad Reza Pahlavi was overthrown in 1979.
While the White House has said nothing is officially planned, spokesman Jay Carney said on Thursday: "It's possible... The extended hand has been there from the moment the president was sworn in."
"We are all watching and listening closely and with interest to the things that the new leadership has been saying," Carney added.
The comments come a day after Rouhani told NBC News that Iran did not seek war and would never develop nuclear weapons.
Other signs of Iranian's renewed effort to work with the West include Wednesday's decision to release 12 political prisoners, and a recent exchange of letters between Rouhani and Obama.