UNHCR sources told Reuters that the new role would be as Special Representative on the Afghan refugee situation.
But Jolie, who has served for 10 years as goodwill ambassador for the U.N. High Commissioner for Refugees (UNHCR), declined to be specific, telling reporters in Geneva: "We are looking at a few countries in the world.
"We're hoping to discuss it in the next few weeks but we want to research it properly and do it well," she said after addressing a meeting of UNHCR's Executive Committee.
Antonio Guterres, U.N. High Commissioner for Refugees, told the talks that Jolie would be his "special envoy" for dramatic situations "in order to mobilise strong international support".
UNHCR sources told Reuters that her new role, expected to be formally announced in coming days, would involve working with the governments of Afghanistan, Pakistan and Iran on the Afghan refugee issue. Pakistan and Iran together host 2.7 million Afghan refugees who have fled their homeland, according to the agency.
On Monday, Jolie made a surprise appearance at the UNHCR's ceremony to honour a Yemeni aid group credited with rescuing thousands of desperate Somali and other African refugees who arrive in Yemen each year on perilous boats.
(Reporting by Stephanie Nebehay, editing by Paul Casciato)