The possible banning comes amid calls by pro-military political forces to brand the Brotherhood a "terrorist organization."
"We are calling for declaring the Brotherhood as a terrorist group," said Mohammed Abdel-Aziz, one of the leaders of the Tamarod youth movement that had organized mass rallies calling for Morsi's ouster.
The military-backed government has declared a state of emergency and imposed a dusk-to-dawn curfew since Wednesday, empowering army troops to act as a law enforcement force. Top Brotherhood leaders, including Morsi, remain held on a variety of charges, including inciting violence.
Since Morsi was deposed in the popularly backed military coup, the Brotherhood has stepped up its confrontation with the new leadership, rallying thousands of supporters in sit-ins and vowing not to leave until Morsi is reinstated.
After security forces broke up the protest camps, Islamist supporters stormed and torched churches and police stations. In response, the interim government authorized Egypt's security forces to use deadly force against those attacking vital government institutions.
On Saturday, Egypt's Interior Ministry said in a statement that a total of 1,004 Brotherhood members had been detained in raids across the country and that weapons, bombs and ammunition were confiscated from the detainees.
Several foreigners were also rounded up including Sudanese, Pakistanis and Syrians, the Interior Ministry said.
Morsi himself has been held incommunicado since his ouster. Top Brotherhood leaders including General Guide Deputy Khairat el-Shater were detained last month.