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Prodi's designation should be approved by the Security Council and announced Tuesday if none of the 15 members object.
The decision to name an envoy emerged from a meeting on the Sahel and Mali that was held on the sidelines of the recent UN General Assembly.
Prodi, 72, served as Italy's prime minister from 1996 to 1998 and again from 2006 to 2008. In between those stints he was president of the European Commission, the European Union's executive arm.
Mali and its West African neighbors want the United Nations to endorse a pan-African military intervention to recapture the north of Mali, which is controlled by Islamist militia.
France has said it will soon present the Security Council with a proposed resolution to pave the way for UN to give the green light to such an intervention.