However, Trump, who in 2018 pulled the U.S. out of a now moribund nuclear deal between Tehran and world powers, repeated a threat of military action against Iran unless a new pact is swiftly reached to prevent it developing nuclear weapons.
Trump, in an April 22 interview with Time magazine published on Friday, said "I think we're going to make a deal with Iran" following indirect U.S.-Iranian talks last week in which the side agreed to draw up a framework for a potential deal.
The Republican U.S. president, speaking separately to reporters at the White House on Friday, reiterated his positive prognosis, saying: "Iran, I think, is going very well. We'll see what happens."
A U.S. official said the discussions yielded "very good progress."
Asked by Time whether he was open to meeting Iranian Supreme Leader Ali Khamenei, an anti-Western hardliner who has the last say on all major state policies, or reformist President Masoud Pezeshkian, Trump replied: "Sure."
Expert-level talks are set to resume on Saturday in Oman, which has acted as intermediary between the longtime adversaries, with a third round of high-level nuclear discussions planned for the same day.
Israel, a close U.S. ally and Iran's major Middle East foe, has described the Islamic Republic's escalating uranium enrichment programme - a potential pathway to nuclear bombs - as an "existential threat".
Israeli Prime Minister Benjamin Netanyahu has called for a complete dismantling of Iran’s nuclear capabilities, saying partial measures will not suffice to ensure Israel's security.
Asked in the interview if he was concerned Netanyahu might drag the United States into a war with Iran, Trump said: "No."
'I'LL BE LEADING THE PACK'
However, when asked if the U.S. would join a war against Iran should Israel take action, he responded: "I may go in very willingly if we can't get a deal. If we don't make a deal, I'll be leading the pack."
In March, Iran responded to a letter from Trump in which he urged it to negotiate a new deal by stating it would not engage in direct talks under maximum pressure and military threats but was open to indirect negotiations, as in the past.
Although the current talks have been indirect and mediated by Oman, U.S. and Iranian officials did speak face-to-face briefly following the first round on April 12.
The last known face-to-face negotiations between the two countries took place under former U.S. President Barack Obama during diplomacy that led to the 2015 nuclear accord.
Western powers accuse Iran of harbouring a clandestine agenda to develop nuclear weapons capability by enriching uranium to a high level of fissile purity, above what they say is justifiable for a civilian atomic energy programme.
Tehran says its nuclear programme is wholly peaceful. The 2015 deal curbed its uranium enrichment activity in exchange for relief from international sanctions, but Iran resumed and accelerated enrichment after the Trump walkout in 2018.
