The meeting -- which would be closed-door consultations -- could take place later in the day, they said.
The request comes one day after a bloody crackdown by Egyptian security forces on protesters backing the deposed Islamist president Mohamed Morsi, which left more than 500 people dead.
France, Britain and Australia are three of the 15 countries currently sitting on the Security Council. France and Britain are permanent members.
One diplomat said that the joint request had been submitted to Argentina, which currently presides over the council. The diplomat added that a Council statement was not likely.