The seven countries including Egypt, Kazakhstan, Senegal and Sweden want UN Secretary-General Antonio Guterres to brief the council on Myanmar's military campaign against Rohingya Muslims in Rakhine state.
The Ethiopian presidency of the council said it was holding consultations to set a time for the meeting, AFP reported on Friday.
The United Nations says more than 420,000 Rohingya have fled for safety to Bangladesh in the face of the army campaign in Rakhine that includes rape and the burning of villages.
The military operation was sparked by attacks carried out by Rohingya militants on police posts on August 25.
The Security Council has called for an end to the violence but rights organizations have said the exodus has continued, fueling international outrage.
The United Nations has described the military operation as "ethnic cleansing" and French President Emmanuel Macron went further, describing it as "genocide."