The US is preparing to reinstate all the sanctions lifted under the deal, the newspaper reported, citing a source briefed on the conversation.
Mr Trump also intends to slap on additional economic penalties, it reported.
The move goes much further than many predicted - and throws the entire agreement into uncertainty.
However a French official denied the New York Times report, claiming the US president did not inform Mr Macron of his final decision.
The two leaders spoke over the phone on Tuesday afternoon ahead of the US president's announcement from the White House.
Senior British diplomats have also said the UK government is "deeply pessimistic" about Mr Trump's announcement over the Iran nuclear deal this evening.
Mr Macron lobbied the US President to stay in the accord during his State Visit - the first of Mr Trump's administration - but appeared unable to convince him.
The two leaders discussed "issues related to peace and stability in the Middle East" during their phone call on Tuesday, Mr Macron's office said.
Other European officials have also rushed to Washington over the last few weeks in a bid to convince Mr Trump to stay in the agreement. Angela Merkel, the German Chancellor, and Britain's Foreign Secretary Boris Johnson have both travelled to the US capital hoping to persuade the US government.
The British government has said it will continue to honour the deal, despite believing Mr Trump will renege on the deal.
The Telegraph
