Several members of the Fine Gael parliamentary party have said they believe a general election is possible within weeks or even days.
It follows a meeting of the Fine Gael parliamentary party meeting in Dublin.
While TDs and Senators were reticent afterwards, a number of them speaking privately to RTÉ News said they believed an election was possible in the near future.
Earlier, Taoiseach Leo Varadkar said that as things stand the Cabinet will meet next Tuesday and the Dáil will reconvene on Wednesday, adding that he will let people know if there is any change to those plans.
Speaking before the parliamentary party meeting in Dublin, Mr Varadkar said he has always favoured a summer election, but added that was a personal preference.
He said the most important thing was to have an election at the right time for the country.
Mr Varadkar said his meeting with Fianna Fáil leader Micheál Martin last night went well, but it had been agreed to keep discussions confidential.
The Taoiseach described himself as a decisive politician, who always takes account of all the factors involved, and one who takes advice.
He said often when people make quick decisions they get the accolade for being decisive, but they are sometimes the wrong decisions.
The Independent Alliance TDs met the Taoiseach in Government Buildings tonight.
The meeting lasted around 20 minutes and there is likely to be a further meeting on Tuesday.
The indications from the discussions suggest that no final decision has been made yet on the timing of the general election.
Earlier, Fianna Fáil finance spokesman Michael McGrath said he did not fear a general election and his party hoped there was an organised and planned end to this Dáil and "not a chaotic" one.
Speaking on RTÉ's Morning Ireland, Mr McGrath said this perspective was outlined by Mr Martin during his talks with Mr Varadkar.
He said: "We see the rising of the Dáil on the 9th of April for the Easter break as the natural end point and there are critical pieces of legislation which we would regard as a priority, that we think can be advanced and completed in this period."
He said it was ultimately a decision for the Taoiseach to decide.
The talks between Mr Varadkar and Mr Martin explored the possibility of agreeing some pieces of legislation that could be passed in the next Dáil session.
In a statement afterwards, both parties said they "discussed Dáil numbers" - a reference to the difficulty that the Fine Gael-led minority is facing getting legislation passed due to its reduced majority.
The two party leaders also talked about "possible legislative proposals which could be passed in a further Dáil session" - that is a shortlist of priority bills that could be passed before the general election.
There was no reference to the possible date of a general election. If an an agreement is not reached, it is widely expected that an election will be held in early to mid-February.
Mr Varadkar and Mr Martin will meet again next week.