The two will hold the meeting on the sidelines of the 15th Association of South East Asian Nations (ASEAN) India summit and the 12th East Asia Summit in the Philippine capital.
The two leaders also met briefly on Sunday as they arrived for the event.
Later, PM Modi and Trump also posed for a family photograph with others leaders, including Canadian Prime Minister Justin Trudeau, Russian Prime Minister Dmitry Medvedev, and Japanese PM Shinzo Abe, participating in the event.
Prime Minister Modi is on a three-day visit to Manila to attend the ASEAN India summit and East Asia Summit on November 14. Terror and Trade related issues will be on top of Modi's agenda during his visit.
Meanwhile, Philippines is the last leg of Trump's five-nation tour of Asia that also took him to Japan, China and South Korea.
Prime Minister Modi will also meet the members of the Indian community at a reception to be hosted by the Indian envoy in Philippines. He will also visit the international rice research institute and the Mahavir Philippines Foundation. (ANI)