Talks between Tehran and world powers aimed at bringing the Joint Comprehensive Plan of Action back to life are ongoing.
Mr Moore, head of the Secret Service Intelligence Service known as MI6, said he is convinced Mr Khamenei is not keen on a return to the deal but said that Iran would not try to halt the negotiations either. He said he still believed the deal was the best way to constrain the Islamic republic’s nuclear capabilities.
Under the previous deal, Iran had scaled back its nuclear programme in return for relief from economic sanctions.
"I'm not convinced we're going to get there ... I don't think the supreme leader of Iran wants to cut a deal," Mr Moore told the Aspen Security Forum in Colorado.
Still, Mr Moore said: "The Iranians won't want to end the talks either, so they could run on for a bit."
The Iranian economy has been suffering from under sanctions reimposed after US president Donald Trump pulled Washington out of the accord in 2018.
Since then, Iran has breached many of the deal’s limits on its nuclear activities and it is enriching uranium close to weapons grade.
Western powers say Iran is getting closer to being able to sprint towards making a nuclear bomb. Iran denies this is its intention.
US President Joe Biden’s administration has sought to revive the deal but American, British and French diplomats all blame Iran for failing to renew the pact after more than a year of discussions.
"I think the deal is absolutely on the table,” Mr Moore said. “And the European powers and the [US] administration here are very clear on that. And I don't think that the Chinese and Russians, on this issue, would block it.
“But I don't think the Iranians want it.”
Iran has described the talks as positive while pointing the finger of blame at the US for failing to provide guarantees that a new administration in the White House would not again abandon the deal as Mr Trump chose to do.
Speaking later in the day at the forum, Israel's defence minister Benny Gantz said Israel, as a last resort, had the military capability to prevent Iran from obtaining a nuclear weapon, if it came to that.
Israel regards any future Iranian nuclear weapons capability as a major existential threat.
"Should we be able to conduct a military operation to prevent it, if needed?” Mr Gantz said. “The answer is yes.
“Are we building the ability? Yes.
“Should we use it as a last [resort]? Yes.
“And I hope that we will get United States' support.”
Bahrain's Undersecretary of Political Affairs Sheikh Abdulla bin Ahmed Al Khalifa declined to directly answer a question about whether his country might participate in pre-emptive military action against Iran's nuclear programme.
But when asked whether it would be fair to interpret his answer as "an ambiguous maybe", he said: "Fair enough."
Bahrain is home to the US Navy's Fifth Fleet headquarters, which oversees American naval operations in the Middle East.
The Iran nuclear deal was hailed as a landmark achievement that would make the world a safer place when it was signed by the Barrack Obama administration and world powers in 2015.
The pact seemed colse to be revived in March but talks were thrown into disarray, partly over whether the US might remove the Islamic Revolutionary Guard Corps (IRGC), which controls elite armed and intelligence forces that Washington accuses of a global terrorist campaign, from its foreign terrorist organisation list.
Mr Biden's administration has made clear it has no plan to drop the IRGC from the list.
Such a step would have limited practical effect but it would anger many American legislators.