The person, who spoke on condition of anonymity, said the UN access would be based on consultations between the six powers and Iran under the draft deal, which would impose limits on the Iranian nuclear program in return for economic sanctions relief.
The foreign ministers of Britain, China, France, Germany, Russia and the United States met for about an hour just after midnight as they struggled to complete the agreement, which has been under negotiation for more than 20 months.
An agreement, if one can be reached, could mark a watershed in Tehran's relations with Western nations, which suspect that Iran has used its civil nuclear program as a cover to develop a nuclear weapons capability. Iran denies this.
A comprehensive meeting between Iran and the powers will be held at 0800 GMT on July 14 (4.00 a.m. EDT), the semi-official Fars news agency reported. Iran's Foreign Minister, Mohammad Javad Zarif, and EU's Foreign Policy Chief Federica Mogherini are expected to read a joint statement.
"Iran and the six powers will hold a comprehensive meeting at the UN headquarters in Vienna at 1000 am local time," Fars said.
The possible agreement, sketched out in a preliminary accord on April 2, would limit Iran's nuclear program for more than a decade in exchange for the gradual suspension of economic sanctions that have slashed Iran's oil exports and crippled its economy.
The marathon nuclear negotiations, which have been going for more than two weeks in Vienna, missed a midnight deadline on July 13 to reach a final deal, but diplomats from all sides said they hoped for a breakthrough in the coming hours.