The Social Democrats believe that a left-leaning minority government is "unlikely" to be formed.
The party's six TDs, including its four new members after the election, met in Leinster House today to agree their priorities ahead of discussing coalition options with other parties.
Ms Shortall, a co-leader, insisted that Social Democrat priorities, including on affordable housing and health, would have to be set out with targeted deadlines in any government deal.
Ahead of meeting Sinn Féin leader Mary Lou McDonald, she played down the prospects of a left-wing minority coalition that relied on outside support from either Fine Gael or Fianna Fáil.
“I think it is unlikely. Confidence and supply didn't work very well in the last Dáil and I think it is unlikely to be a composition in this Dáil."
Ms Shortall stressed that these were “exploratory talks” and not negotiations.
The party leadership is also set to meet Fianna Fáil leader Micheál Martin, Labour leader Brendan Howlin and Green leader Eamon Ryan this week.
Ms Shortall added: “Obviously a centre-left government would be our preference. It depends on whether the numbers are there or not.
The party wants these areas addressed but with targeted progress.
Co-leader Catherine Murphy explained: “It is all about outcomes, timelines. It is not just a question of a list.”
Ms Murphy also confirmed the issue of the party's leadership and whether there should be just one leader for the Social Democrats would form part of an internal review in the year ahead.
She welcomed the four new TDs, Wicklow's Jennifer Whitmore, Dublin Bay-North's Cian O'Callaghan, Dublin Central's Gary Gannon and Cork South West's Holly Cairns and said their capabilities would be noticed in the new Dáil.
Ms Shortall joked about the trebling of the party's parliamentary size: “We no longer fit in a phonebox.”