No date has been set yet.
As chairman, Dunford is the chief military advisor to the President. In the past, chairmen have met with incoming Presidents.
There may be more than one meeting between the two, if Trump wants, the official said.
Dunford will be prepared to discuss how US forces are arrayed around the world and any other topics Trump is interested in, the official added.
The two men informally greeted each other at this weekend's Army-Navy football game. Along with Dunford, Trump also briefly met Gen. Mark Milley, chief of staff of the US Army, Adm. John Richardson, chief of naval operations, and Gen. Robert Neller, commandant of the Marine Corps. The encounter with between Trump and the chiefs was brief and limited to social pleasantries, the official said.
Dunford and Trump had already met on at least one occasion, at an April 2015 private charity dinner in New York.
Dunford hinted at his approach to the Trump administration during recent remarks, saying that while "significant progress" has been made against ISIS -- limiting the territory it holds and disrupting its external operations -- "there are some things that we would probably bring in to the new administration for consideration."
Two defense officials told CNN that any changes are likely for now to be fairly routine, centered around potential options such as giving the military the authority to conduct missions more quickly with less oversight by the White House. But any substantive change in the war against ISIS might require US combat forces, something the Pentagon has been unenthusiastic about.
The Joint Chiefs, along with warfighting commanders around the world, are finalizing a new classified military strategy they plan to present to Trump detailing the military challenges to the US.
The report was long underway and was not created for Trump. But it is now expected to be a key foundation for any decisions Trump may make.