The official, who spoke on condition of anonymity, said all seven nations involved in the talks were committed to a self-imposed June 30 deadline but it was possible that could slip if necessary to get the substance of any agreement right.
U.S. Secretary of State John Kerry flies to Vienna on Friday to join the negotiations among Iran, the United States and five other nations: Britain, China, France, Germany and Russia.
The nations are seeking to reach a deal under which Iran would curb its nuclear program in exchange for relief from economic sanctions that have crippled its economy.
The United States and some of its allies suspect that Iran is using its civil nuclear program as a cover to develop a nuclear weapons capability. Iran says its program is solely for peaceful purposes, such as making medical isotopes.
The two main sticking points in the talks are the timing and scope of sanctions relief and the monitoring and verification measures needed to ensure Iran does not cheat on an agreement.
"Despite these tough issues, we can truly see a path forward that gets us to a very good agreement here," the senior U.S. official told reporters during a conference call. "I am hopeful but it still remains to be seen whether we can get there."
The official also raised the possibility, as have many others, that the June 30 deadline could slip.
"We are committed to the deadline of June 30, even if we miss it by a short bit, which we may," the official said. "What matters here is the substance of the deal and we have get it right."