Leo Varadkar has refused to be drawn on whether he would demand a rotating Taoiseach arrangement in any coalition deal with Fianna Fáil.
It is widely expected another term as Taoiseach would be one of the demands of Fine Gael in exchange for its support.
Tomorrow Mr Varadkar and Micheál Martin meet to hold exploratory talks on possibly coming together to form a government.
It is early days, but already there are some roadblocks, one being the idea of a rotating Taoiseach, which Fine Gael is likely to demand.
A number of Fianna Fáil TDs have suggested that cannot happen and Mr Varadkar has said it is too early to even be thinking about it.
He said: "I think we are getting way ahead of ourselves here, Fine Gael is preparing for opposition and all we are doing this week is engaging in some exploratory talks with Fianna Fáil and the Greens and we'll see how they go."
Meanwhile tonight Sinn Féin will hold the first of three rallies planned for this week.
Mr Varadkar has said they are unwelcome, but Sinn Féin's Pearse Doherty dismissed concerns
Mr Doherty said: "These types of hysterics from Leo Varadkar is nothing but that, hysterics. What we are doing is engaging with the public. We are elected representatives, we have a huge mandate and we are going out in public meetings to talk to the public and to answer questions."
The first of those Sinn Féin rallies gets underway in Cork at 7.30pm.