Three senior member of the Fine Gael party are thought to be in the running to become the next EU Commissioner.
Simon Coveney is reportedly the Government's favoured candidate.
MEPs Mairead McGuinness and Frances Fitzgerald are also named.
Phil Hogan resigned from the post earlier this week, saying the public discussion around the Oireachtas Golf Society Dinner was a 'distraction.'
Labour Senator Ivana Bacik says the government should nominate a man and a women, as they were asked to.