ElBaradei met with interim President Adly Mansour for two hours yesterday afternoon, and "discussions and consultations are ongoing," presidential adviser Ahmed al-Muslimani said on state-run TV.
"Tomorrow we expect to name the prime minister and the ministers."
He added that ElBaradei was "the logical choice" among a list of names being considered.
If 71-year-old ElBaradei is selected, it would signal a secular shift just days after a military coup ousted nation's first democratically elected and Islamist president Mohamed Morsi.
A coalition supporting 61-year-old Morsi's reinstatement called for protests today to reject Wednesday's "military coup" by Egyptian Defence Minister Abdel-Fattah El-Sisi.
Officials had earlier named ElBaradei, a former head of the UN's nuclear watchdog, for the post of Prime Minister. News of his appointment had been criticised by the Salafist Nour Party, which said it would not work with him.
The appointment of ElBaradei caused anger among supporters of Morsi, who want to see him returned to power.
The celebrations came after 24 hours of violence that left 37 people dead and over 1,400 injured.
The possible appointment of ElBaradei, the defacto head of the opposition movement in the days leading to Wednesday's ouster of Morsi, has been discussed as a possibility among supporters in recent days.
