Morsi, the candidate from the Muslim Brotherhood's Freedom and Justice Party, was declared the winner of a runoff election last weekend. He beat retired air force general and former Prime Minister Ahmed Shafiq to become the first democratically elected president in Egyptian history.
Shukry Fouad, co-founder of a political organization led by ElBaradei, said Morsi didn't offer the reformer the post of prime minister or any other formal position, Egyptian news service al-Ahram reports.
A constitutional panel met this week to determine if a post-revolution Egypt would have a presidential, parliamentary or mixed political system. As of yet, there is no defined role for the president.
A series of political moves taken by the ruling military council before the runoff vote prompted ElBaradei to describe the current situation in Egypt as "a total mess."
Morsi is expected to take the oath of office this weekend.