President Barack Obama recently told Spain's Telemundo network that Iran's new president appears open to dialogue.
Obama and Iranian President Hassan Rouhani could meet Tuesday, the same day the two leaders are scheduled to address the U.N. General Assembly.
The men have already exchanged letters and it's raising expectations for a thaw in the countries' tense relations.
A longstanding dispute over Tehran's nuclear program is at the heart of the U.S.-Iran impasse.
"There is an opportunity here for diplomacy," Obama said, "and I hope the Iranians take advantage of it."
"There are indications that Rouhani…is somebody who is looking to open dialogue with the West and with the United States in a way that we haven't seen in the past," Obama said. "And so we should test it."
But political observers say the although Rouhani presents himself as a moderate, he is really just playing for time to allow Iran to develop nuclear weapons.