It is more likely than not that there will be a united left-wing candidate running in the presidental election later in the year, according to People Before Profit-Solidarity TD Paul Murphy.
Mr Murphy said that he does not believe it is true to say that Sinn Féin is certain to run its own candidate.
A meeting on the issue could take place next week and significant progress on the matter is possible before the Dáil recess on 17 July, he aded.
Mr Murphy would not be drawn on likely candidates, adding with a laugh that he had no comment to make on Joe Duffy.
The broadcaster said last week that he had not approached about running for Áras an Uachtaráin.
Earlier, Social Democrats TD Rory Hearne also talked up the prospect of a united-left candidate saying it would offer voters the chance to "give expression" to social issues in the presidential election.
Meanwhile, the Taoiseach has declined to say if Fianna Fáil will select someone to challenge for the job, saying: "We will take our decision in due course".
Speaking during a visit to Japan, Mr Martin said that his party did not run a candidate in the past two presidential elections, is "examining the situation" and, accordingly, it is "a bit premature" to make any announcement.
However, he pointedly referenced a comment expressed by former Labour leader Joan Burton that any party "shouldn't announce anything" until the end of August.
