The leaders of five left and liberal leaning Dáil parties met this evening to discuss supporting a combined presidential election candidate.
While no decision has been made, RTÉ News understands that the Social Democrats and People Before Profit-Solidarity made it clear during the meeting that they are increasingly open to Independent TD Catherine Connolly potentially entering the race.
This view is understood to have been expressed by Social Democrats TD Cian O'Callaghan and People Before Profit-Solidarity TD Paul Murphy at the 30-minute meeting in Leinster House this evening.
However, during the same meeting Sinn Féin leader Mary Lou McDonald and Labour leader Ivana Bacik are understood to have made it clear their parties are still taking part in internal processes on whether to run their own candidates or support a combined left contender.

The meeting, which was one of a number to have taken place since late spring, was also attended by Green Party leader Roderic O'Gorman, who is understood to have said while he is open to a discussion on a Catherine Connolly candidacy, he wants to see a detailed plan for what any combined party platform would involved before any decision is made.
While party leaders confirmed further meetings are likely, a number expressed the view that this could be in late August or early September, at which time one or more candidates may have formally entered the race.
The growing interest in a potential Catherine Connolly candidacy came hours after Independent TD Brian Stanley called on all Opposition parties to unite behind the Galway West TD as a presidential candidate.
Mr Stanley said the presidency can only be won by the Opposition if they have a single agreed-upon candidate.
"Left and opposition TDs must unite to ensure a progressive candidate is elected in the upcoming presidential election.
"Failure to do so will allow the establishment parties to not just control the Dáil and Seanad but also the third element of our Oireachtas, the presidency," he said.
Fine Gael this week opened its nomination process for the presidential election. Fianna Fáil is also currently finalising its own decision on whether to run a candidate, while a number of other potential Independent candidates have expressed varying degrees of interest.
To formally become a presidential candidate, an individual must either receive the support of four local authorities or else the backing of at least 20 TDs and senators.