In an interview with a US broadcaster at the UK consulate general's residence in New York, he criticised the existing deal, stating it was “bad” and had “many defects” from previous UK policy.
"If it was a bad deal, and I'm willing to accept that it had many, many defects, then let's do a better deal," the PM said.
"And I think there's one guy who can do a better deal and one guy who understands how to get a difficult partner like Iran over the line and that is the president of the United States.
"So I hope that there will be a Trump deal, to be totally honest with you."
Mr Johnson is due to meet with Iranian president Hassan Rouhani and President Trump on Tuesday, in separate meetings.
Mr Johnson’s comments on the UK’s current policy – the Joint Comprehensive Plan of Action (JCPoA) – earned him the praise of the president, who said the PM was “a winner”.
However, Downing Street moved to stress that Mr Johnson supports the current nuclear deal.
"The PM supports the JCPoA," a Government spokesman said.
"The Iranians aren't currently in compliance and we need to bring them back into compliance. If there's a way to do that, we're open to discussing possible solutions."
This comes as the PM has joined the US and Saudi Arabia in formally blaming Iran for attacking a Saudi oil facility last week, while also dismissing claims by Yemen's Houthi movement that it was behind the Aramco attacks.
However, the PM has said military force over Iran is "not something that I think will necessarily help the situation".
He was talking after a terse exchange of words with Iran, saying Iran was responsible for the Aramco attacks with a"very high degree of probability".
"We think it very likely indeed that Iran was indeed responsible for using both UAVs (unmanned aerial vehicles), both drones and cruise missiles," Mr Johnson said.
Iran countered by rejecting the PM's remarks and criticising "fruitless efforts against the Islamic republic of Iran".
"The British Government should stop selling lethal weapons to Saudi Arabia" over the war in Yemen, foreign ministry spokesman Abbas Mousavi said to the semi-official ISNA news agency.
The US and Saudi Arabia had already accused Iran of being behind the September 14 raids on the world's largest oil processor and an oil field, causing a spike in prices.
The PM said he would "follow very closely" American proposals to do more to defend Saudi Arabia, with Tehran's ire being further provoked by the US-led coalition patrolling the region's waterways.
The UK has also dismissed comments from Yemeni Houthi rebels, in which they claimed responsibility for the attack on the oil facilities.
A Whitehall source said: "Imagery from the site of the attack shows the remnants of Iranian-made land attack cruise missiles and the scale, sophistication and range of the attack is inconsistent with the Houthis' capability."
Mr Johnson said he would also bring up the case of Nazanin Zaghari-Ratcliffe and other dual nationals being held in Tehran when he meets Mr Rouhani on Tuesday.
Mr Johnson said: "In the course of my conversation with President Rouhani, I will not only be discussing Iran's actions in the region, but also the need to release not just Nazanin but others who in our view are being illegally and unfairly held in Tehran," he said.
The British-Iranian aid worker is midway through a five-year jail sentence for spying charges, which she has always denied.
The PM has always faced intense criticism over his handling of her case during his time as foreign secretary,particularly when it was revealed he mistakenly told a Commons committee Mrs Zaghari-Ratcliffe was in Iran “teaching people journalism”.
Iranian authorities cited his words as evidence she was spreading propaganda against the Islamic republic.