A statement by the Supreme Judiciary Council carried by the official MENA news agency urged Talaat Abdullah "to express a wish" to return to his previous job as a judge for the sake of the unity of the judiciary.
Abdullah's appointment was decried as illegal by many judges and fellow prosecutors. It has led to days of protests outside his office in downtown Cairo by judges and prosecutors. The protests late last year forced him to tender his resignation, but he eventually withdrew it and stayed in office.
A court ruling last week annulled the presidential decree appointing Abdullah, but he has continued to carry out his duties. The presidency said last week it was still considering whether to appeal the ruling.
There was no word immediately available from Abdullah on his plans.
Removing Abdullah has been a key demand of the mostly liberal and secular opposition and Sunday's advice by the council of the judiciary appeared aimed at offering him an honorable exit and to end a long running crisis within the judiciary over his appointment.
Abdullah has over the past two weeks issued summons against several media celebrities critical of Morsi, Egypt's first freely elected president. They included popular TV satirist Bassem Youssef, who was accused of insulting Morsi and Islam.
Youssef's questioning last week, plus earlier arrest warrants issued by Abdullah's office for five rights activists, has created tension between Egypt and the United States. The satirist was released on bail.