Trump has branded the accord the “worst” deal ever backed by the US and will decide on May 12 whether to reimpose sanctions and effectively torpedo the international alliance behind the deal.
But the British Foreign Secretary, who is visiting the US this week, is trying to persuade the president not to pull out of the long-fought for agreement.
Johnson said that, if he backs the Iran deal, Trump has as much chance of winning the award as Barack Obama.
Speaking to Sky News, Johnson said: “If he can fix North Korea and if he can fix the Iran nuclear deal then I don’t see why he is any less of a candidate for the Nobel Peace Prize than Barack Obama, who got it before he even did anything.”
Johnson is meeting the US Secretary of State Mike Pompeo but is not scheduled to hold talks with Trump this week.
Instead, he appeared on the president’s favourite TV programme in an effort to save the deal.
Speaking on Fox and Friends on Monday morning, the Tory minister said the president should not “throw the baby out with the bathwater” by tearing up the Iran nuclear deal.
Johnson said: “What if the Iranians do rush for a nuclear weapon? Are we seriously saying that we are going to bomb those facilities at Fordo and Natanz?
“Is that really a realistic possibility? Or do we work round what we have got and push back on Iran together?”
It is not the first time a foreign politician has tried to communicate with Trump by slightly unorthodox means.
Last month Israel’s Prime Minister Benjamin Netanyahu delivered a very basic powerpoint presentation, claiming Iran had continued gathering nuclear knowledge after signing a 2015 agreement.
Netanyahu stood in front of two words written in giant Times New Roman letters: “Iran lied”. Many felt the message was aimed specifically at Trump.
The US President has also been known to call into Fox and Friends to weigh in on discussions, with his latest tirade directed at the “dishonest media” in a rant that made even the show’s hosts look embarrassed last week.
British, French and German diplomats have been working for weeks behind the scenes with US counterparts in an effort to preserve the Iran deal.
Trump has threatened to withdraw from the Joint Comprehensive Plan of Action (JCPOA) deal signed by the US, China, Russia, Germany, France and Britain with Iran.
Under its terms, Iran is committed to a peaceful nuclear energy programme.
But Trump has been a vocal critic of the agreement and in January issued an ultimatum to “either fix the deal’s disastrous flaws, or the United States will withdraw”.