Morsi's supporters are threatening to force their way into the square.
The possibility of bloodshed on an occasion revered by most Egyptians is seen as a sign of the schism that began to surface soon after Morsi's narrow election victory in June 2012.
He was ousted in a July 3 coup that followed demonstrations by millions of Egyptians demanding that he step down.
Sunday's faceoff will be the latest episode in the turmoil roiling Egypt since Mubarak's ouster in February 2011.
The military-backed government has since Morsi's departure rounded up at least 2,000 members of his Muslim Brotherhood, including most of the Islamist group's leaders.
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