"I'm always open. I have no plans to meet with them, but I'm always open," Trump said Sunday in Houston, when asked if he was open to hearing Rouhani's plan.
Rouhani departed for New York on Monday to attend the annual gathering of world leaders at the United Nations.
The president is slated to deliver a speech at the 74th UN General Assembly meeting on Wednesday.
Asked about a meeting with Rouhani, Trump told reporters he would meet if Iranians wanted "but I have absolutely no plans to meet."
"We'll see what happens. Certainly, the United Nations Week is going to be very interesting. I look forward to it," he added.
On Sunday, the Iranian president unveiled a new initiative for security of the Persian Gulf and the Sea of Oman, saying the “Coalition of Hope” scheme will be put forward in the forthcoming meeting of the United Nations General Assembly.
“This year, we will be putting forward a plan at the United Nations, according to which the Islamic Republic of Iran --in cooperation with the regional countries-- can ensure security in the Persian Gulf and the Sea of Oman with the help of the region’s countries,” the president added.