Minister for the Environment John Gormley has said he believes it would be 'very ambitious' to try to hold a referendum on the future of the Seanad on the same day as the General Election.
There has been much debate on the future of the Upper House in the past week.
Speaking on RTÉ's Morning Ireland, Mr Gormley said it would be difficult to frame such a complex piece of legislation in a short time.
Minister for Defence Tony Killeen said the issue would be discussed by the Cabinet, while Minister for Enterprise Batt O'Keeffe said speculation about the date of a referendum would be pointless before that discussion took place.
Mr O'Keeffe said it was not on the top of the Government's agenda.
Green Party Chairman and Senator Dan Boyle has said he thinks it is 'unlikely' there will be a vote on that day.
Speaking on RTÉ's News at One, Labour Party leader Eamon Gilmore said a convention to examine constitutional reform will be part of the proposals being published by Labour on Thursday.
He said it was in this context of reform that the Labour Party supported abolition of the Seanad.
Fine Gael and Labour had both previously said that they were in favour of the abolition of the Seanad.
