The Taoiseach is expected to seek Cabinet approval tomorrow for a move which would see the Ceann Comhairle elected by secret ballot in the next Dáil.
The suggestion came from the Constitutional Convention.
Other reforms which could be brought in include the election of the chairs of Oireachtas committees based on party strength, rather than appointment by the Government, according to the Irish Times.
Tomorrow's Cabinet meeting is the first since Christmas. The change, if approved, would come into effect when the next Government is in place after the forthcoming General Election.
Up to now, the Ceann Comhairle has been elected by open vote shortly after a General Election.