The Western diplomats say the major hurdles to a deal have been overcome, although they acknowledge some important issues needed to be resolved and capitals still needed to sign off. Those loose ends are what are keeping Iranian officials from sounding more optimistic, with a Monday deadline looming.
"There are two or three things that need to be worked out," a senior Iranian official told CNN on Sunday.
But if all goes well, an announcement to come as early as Monday, Western officials said.
"We are nearly there," one Western diplomat said.
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Another said negotiators made good progress over the weekend and the talks were reaching the "endgame."
The Iranian official said whether or not a deal gets struck hinges on the negotiators' appetite for getting it done.
"It only depends on political will," the official told CNN.
Secretary of State John Kerry on Sunday said he is "hopeful" about the U.S. and the other world powers being able to reach a deal with Iran to curb its nuclear program.
This followed a marathon series of meetings in Vienna on Saturday, including two sessions with the 6 allies and Iran -- one going to midnight. There were also separate sessions on Saturday between Kerry, European Union foreign policy chief Federica Mogherini and Iranian Foreign Minister Javad Zarif.
"We had a very good meeting. Positive," Kerry told reporters on Sunday of the previous day's meeting with Zarif. "I think we're getting to some real decisions so I will say -- because we have a few tough things to do. I remain hopeful. Hopeful," he said.
The negotiators, facing another deadline, on Friday extended the talks through Monday. This was the third extension of the final round. The parties also extended the interim agreement, known as the Joint Plan of Action, through Monday.
On Saturday, after one of his meetings with the European negotiator and the Iranian Foreign Minister, Kerry tweeted "Still have difficult issues to resolve."
Met with @FedericaMog and @JZarif this AM. Still have difficult issues to resolve. #IranTalksVienna
1:39 PM - 11 Jul 2015
A Western diplomat told CNN on Sunday "good progress" has been made and said negotiations are "in the endgame but not finally finalized."The diplomat said talks "should be finished by tomorrow."
Another source close to the negotiations described them as a "Work in progress, still some issues to be closed."
Several of the European foreign ministers had left Vienna late last week, but have since returned.
French Foreign Minister Laurent Fabius, who just arrived back to the Iranian nuclear negotiations in Vienna, said he was optimistic the talks were nearing completion.
"I hope we are finally entering the final phase of these marathon negotiations," he told reporters, outside the Palais Coburg. "I believe it."
In another signal that talks are entering a critical stage, Russia's Foreign Minister Sergey Lavrov is en route to Vienna to join negotiations, according to a tweet in Russian issued by Russia's Foreign Ministry.
But a senior State Department official cautioned against too much optimism at this stage.
"We have never speculated about the timing of anything during these negotiations, and we're certainly not going to start now - especially given the fact that major issues remain to be resolved in these talks," the official told CNN.
And a top Iranian official called reaching a deal on Sunday "logistically impossible."
We are working hard, but a deal tonight is simply logistically impossible. This is a 100 page document,after all.
5:16 PM - 12 Jul 2015
"We are working hard, but a deal tonight is simply logistically impossible. This is a 100 page document, after all", Iranian Foreign Ministry official Alireza Miryousefi tweeted, citing a senior Iranian official.
By CNN
