The defence lawyers have demanded that the judges in two of three trials underway against Morsi withdraw, after private conversations between the defendants and their lawyers were allegedly taped and a newspaper leaked one between Morsi and lawyer Selim al-Awa.
In one of the trials, Morsi and others are accused of breaking out of jail during the 2011 uprising that toppled veteran president Hosni Mubarak.
The second trial concerns accusations of espionage against the Islamist president, who was deposed by the army last July following massive protests against his one-year rule.
He is also to face a fourth trial for insulting the judiciary, but no date has yet been announced.
The trials are part of a massive government crackdown on Morsi and his Muslim Brotherhood movement since the army overthrew him on July 3.