"They agreed to meet," UN spokesman Stephane Dujarric said, adding that no firm date had been set for the talks. Ban told AFP in an interview on Friday that he was hoping to meet Trump before he ends his tenure as UN chief on December 31.
Trump won the US presidency on a platform that calls for closer ties with Russia, pulling out of the Paris climate deal, shaking up security alliances and questioning US funding of the United Nations.
His election victory has shocked UN diplomats and notably put a question mark over the fate of the Paris climate deal championed by Ban during his 10 years at the helm of the United Nations.
Ban has downplayed anxiety over a new world order under Trump, saying that as president, the billionaire real estate tycoon will shed the strident rhetoric of the campaign and work to confront global crises like climate change.
"Now, post-election, when he creates his transition team with experts and people with vision and expertise, I am sure that the United States will continue to play a leading role," Ban said.
Ban was in Marrakesh this week to attend climate talks and deliver the message that the hard-fought Paris deal signed by all 193 UN member-states should not be scrapped. He spoke to Trump over the phone on Friday and the two men agreed to remain in contact.
The United States is by far the largest financial contributor to the United Nations, contributing 23 percent of its budget and 28 percent to the peacekeeping budget of some USD 8 billion.
As one of the five veto-wielding Security Council members, the United States is a key player in decisions on all global crises like the wars in Syria, Yemen and the Israeli-Palestinian conflict.