"Let's do a better deal," Johnson said in an interview with NBC while in New York for the UN General Assembly.
"I think there's one guy who can do a better deal... and that is the president of the United States. I hope there will be a Trump deal," added the prime minister.
Iranian Foreign Minister Javad Zarif appeared to respond to Johnson's comments on Twitter, writing that France, Germany and Britain's "paralysis in fulfilling their obligations w/o US permission has been clear since May 2018," when Washington withdrew from the accord.
"No new deal before compliance w/ current one," Zarif added.
Iran and the US have been at loggerheads since May last year, when Trump abandoned the 2015 nuclear deal that gave Iran the promise of sanctions relief in return for curbs on its nuclear program.
Trump then began reimposing sanctions in what his administration dubbed a "maximum pressure" campaign.
European countries that helped negotiate the accord, including France, England and Germany, have been trying to de-escalate tensions in an effort to save the deal.
While France and Germany have not previously taken a clear stance on whether to negotiate a new agreement, French President Emmanuel Macron also appears to be considering abandoning the accord.
"I'm not married to the JCPOA," he told reporters traveling with him to New York, using the deal's acronym.
"It has to be said that the two main players are in the process of deciding to leave it. One has left, the other is telling us that they will leave," Macron added.
Iranian President Hassan Rouhani arrived in New York on Monday afternoon, where he will meet with Macron.
No meeting has been scheduled between Rouhani and Trump, though the American president said he could not rule one out.