A new poll shows voters would prefer Fianna Fáil leader Micheál Martin over Enda Kenny as Taoiseach.
The Millward Brown survey for the Sunday Independent says 39% of people would rather see the Fianna Fáil leader in charge, while 17% would choose Enda Kenny.
The Dáil will vote for a Taoiseach again when it reconvenes on Wednesday, however neither of the men is expected to receive enough votes to secure the office.
The poll also found that 70% of people would not change how they voted if a second General election were called. Fine Gael and Fianna Fáil are due to resume talks with independents tomorrow after taking a break for the weekend.
Meanwhile, a member of Fianna Fáil's negotiating team has rubbished claims that the party is considering entering a partnership Government.
The idea was mooted by Enda Kenny at the end of last week and could see Fine Gael and Fianna Fáil hold ministerial office over the course of a five year term.
Both parties are due to resume negotiations with a variety of Independents tomorrow - before the Dáil votes on a new Toaiseach on Wednesday.
Jim O'Callaghan Fianna Fáil, TD for Dublin Bay South, says his party wants a minority Government: "We're engaged, and have been engaged in talks with Independents for the past two weeks trying to get their support for a Micheál Martin-Fianna Fáil led minority goverment.
“We've had very detailed discussions with them so we're committed to trying to form a Fianna Fáil minority government which is the change that the Irish people voted for.”