Update: Leo Varadkar has become the first person to confirm he'll be in the running to become the next leader of Fine Gael when a contest begins.
The Social Protection Minister is one of the favourites to replace Enda Kenny.
Minister Varadkar says conversations about the Fine Gael leadership are happening, but denies he is currently campaigning.
Earlier: Leo Varadkar has said his personal and family life should not be an "issue" in the Fine Gael leadership campaign, writes Political Reporter Elaine Loughlin.
Mr Vardakar has also signalled that he would not call a snap election if chosen as the next leader as it would not be in "anyone's interest".
Publishing review of Back to Work Enterprise Allowance in Dublin this morning, Mr Varadkar said the leadership race should not be about personalities but "people's vision for the future of the country".
"I am not going to make my personal life or family life an issue in any campaign and I hope and trust others wont do either," the Minister for Social Protection said.
He said the confidence and supply agreement with Fianna Fáil would stand no matter who becomes the next leader of Fine Gael.
"The confidence and supply agreement that was negotiated between Fianna Fáil and Fine Gael stands, it is not just an agreement with the Taoiseach and the party leader, it's an agreement between Fianna Fáil and Fine Gael. I was involved in negotiating that, I was part of the initial discussions back that morning in Jim O'Callaghan's kitchen and it is an agreement between both parties and it will stand no matter who is leader."
Asked whether the change in leadership could signal a snap election to allow Enda Kenny's successor gain a public mandate he said he doesn't think anyone wants an election - "not politicians and not the general public".
He added: "We have an agreement in place with Fianna Fáil based on a confidence and supply agreement, we will honour that, I hope that they would too and of course we have a very good working relationship with Independents.
"I don't think an election in the short term would no serve anyone's interests," Mr Vardadkar said