That figure is just a fraction of the displacement that aid groups expect to see when Iraqi forces reach the city limits and some of the million-plus people thought to be inside attempt to flee.
"Over 10,500 people are currently displaced and in need of humanitarian assistance," the UN's Office for the Coordination of Humanitarian Affairs said in a statement.
While numbers have increased rapidly over the past two days, there was no sign an exodus of larger proportions was beginning.
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"Population movements are fluctuating as the front lines move, including people returning to their homes following improved security conditions in the immediate area," it said.
The aid community has been scrambling to build camps and bring equipment to areas on the edges of the Mosul battlefield, a vast area where Iraqi forces are closing in on jihadists from the north, east and south.
Humanitarian workers fear being overwhelmed by huge outflows when the civilians trapped in Mosul find a way out, in an emergency that could dwarf previous displacement crises in Iraq.
More than 3.3 million Iraqis have had to flee their homes due to conflict since the start of 2014.