The two diplomats cautioned that final details of the pact were still being worked out Sunday afternoon and a formal agreement still awaits a review from the capitals of the seven nations at the talks. They said plans now are for the deal to be announced on Monday.
The diplomats, who are at the talks, demanded anonymity because they were not authorized to discuss the negotiations publicly.
The agreement would cap nearly a decade of diplomacy, including the current round in Vienna that has run more than two weeks and blown through three deadlines.
Even before the envoys spoke to The AP, the nuclear negotiations appeared well on the way to an agreement.
U.S. Secretary of State John Kerry, who on Thursday had threatened to walk away from the negotiations, noted Sunday that "a few tough things" remain in the way of agreement but added "we're getting to some real decisions."
En route to Mass at Vienna's gothic St. Stephens Cathedral, Kerry said twice he was "hopeful" after a "very good meeting" Saturday with Iranian Foreign Minister Mohammad Javad Zarif, who had Muslim services Friday.
French Foreign Minister Laurent Fabius also was cautiously optimistic, telling reporters Sunday: "I hope that we are finally entering the last phase of this negotiation."
The pact is meant to impose long-term, verifiable limits on nuclear programs that Tehran could modify to produce weapons. Iran, in return, would get tens of billions of dollars in sanctions relief.