"We will see what happens", Trump told reporters at the White House when asked about such a possibility.
Trump emphasised that Washington is "not looking for regime change" in Iran. He also said he believes that the two countries can make a "good deal".
At the same time, Trump expressed concern over Iran's nuclear programme.
"We cannot let Iran have nuclear weapons", he said while expressing confidence that US sanctions against the Islamic Republic were working.
The statement comes after US State Secretary Mike Pompeo said a day ago that Trump and Iranian President Hassan Rouhani might hold talks on the sidelines of the UN General Assembly later in September.
Earlier in September, Iran started the third stage of rolling back nuclear obligations under the JCPOA. The third stage, in particular, includes research of the new type of centrifuges beyond the frameworks of the accord.
Tehran then announced that it would start abandoning some parts of its nuclear obligations every 60 days unless European signatories to the deal, including France, ensured Iran's interests under the agreement amid Washington’s reinstated sanctions.
For months, the United States has been stepping up its sanctions on Iran as part of its "maximum pressure" campaign, which aims to force the Islamic Republic to renegotiate the landmark 2015 international nuclear deal.
The Joint Comprehensive Plan of Action (JCPOA), signed in 2015 by Iran, China, France, Germany, Russia, the United Kingdom, the United States, Germany and the European Union, required Iran to scale back its nuclear program and severely downgrade its uranium reserves in exchange for sanctions relief.
On 8 May 2018, US President Donald Trump unilaterally withdrew his country from the deal and began reimposing economic sanctions on Iran. Exactly a year later, Tehran said it would begin reducing its commitments under the JCPOA after 60 days unless the Western signatories took steps to offset the impact of the US sanctions. The Islamic Republic subsequently began scaling back its obligations under the accord every 60 days.