The two sides took part in Omani-mediated talks in the Swiss city this week, with US threats of military action looming over the negotiations.
In an interview with French TV channel LCI, Grossi, the head of the International Atomic Energy Agency said "we made progress, but there is still work to be done, and the problem is that we don't have much time".
"There is the possibility of a dialogue that is really beginning, for the first time, to take shape," he said. "We are starting to talk about concrete things, about what we have to do," the Argentinian diplomat added.
He said he saw "a willingness on both sides to reach an agreement, but obviously such an agreement is enormously complex".
Tehran has suspended some cooperation with the IAEA and prevented the watchdog's inspectors from accessing sites bombed by Israel and the United States during a 12-day war last June, accusing the UN body of bias and of failing to condemn the strikes.
Earlier on Wednesday, the White House warned Iran that it would be "wise" to do a deal, while US President Donald Trump again hinted at military action against the longtime American foe.
Trump first threatened military action against Iran over the authorities' deadly crackdown on anti-government protests in January.
While talks between the two sides have now resumed for the first time since the 12-day war collapsed the last set of negotiations, Washington has continued to build up its military forces in the Middle East.
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