The source, who asked not to be named, told The Anadolu Agency that the Sudanese authorities had given al-Za'tari hours to leave Sudan.
He did not, however, mention the reasons for the move, which the authorities have yet to comment on.
The decision comes only one day after Sudan gave UNDP Sudan Director Yvonne Helle 72 hours to leave as well.
The decision to ask al-Za'tari to leave comes weeks after he allegedly made statements to a Norwegian newspaper deemed by the Sudanese government to be "offensive to Sudan and President Omar al-Bashir."
Al-Za'tari said that he had told the Sudanese government later that he had not told the newspaper that Sudan was a "country in humanitarian and economic crisis and that Sudanese society had become totally dependent on humanitarian aid."
Al-Za'tari was also reported to have told the newspaper that the "international community is compelled to deal with Sudanese President Omar al-Bashir, who is wanted by the International Criminal Court."
The UN official denied this as well, saying the newspaper had committed a professional mistake and had failed to quote him accurately.
The Sudanese government announced last month that it had a plan to replace foreign humanitarian workers with Sudanese personnel. It said the plan would go into effect next year after hammering out a partnership agreement with the UN as far as humanitarian needs were concerned.
Around 21 humanitarian organizations affiliated with the UN are working in Sudan, along with around 104 other foreign organizations. The activities of most of these organizations are based in conflict areas, especially in the southern Darfur region.