Independent TDs have indicated they want five Cabinet posts as Fine Gael and Fianna Fail went back to the negotiating table in the hope of forming a minority government.
Acting Taoiseach Enda Kenny and Fianna Fail leader Micheal Martin spoke on the phone yesterday and agreed to put the drama of the past week behind them.
Sources told the Herald the conversation was "very friendly" and both men are now working towards a government.
However, there will not be a vote on the election of a taoiseach next week, as it is likely to be several more days before a deal between the two parties is agreed.
In the background, Fine Gael is also continuing talks with 14 Independents who they want to be part of government.
Cold water has been poured on Independent Alliance (IA) TD Finian McGrath's suggestion that five or six ministries should be shared between the non-party deputies who vote to return Mr Kenny as Taoiseach,
A senior Fine Gael source said that so many cabinet posts would be too many for Independents to expect, unless all 14 are involved in a new administration.
"It all depends on the size of the government," said the source.
"If we only reach 58 TDs it'll be less, but if we end up with 65-plus then more Cabinet seats would be shared out.
"Those kind of things are impossible to quantify until people sign up."
Dublin Bay North TD Finian McGrath outlined the main issues of concern to his group.
These were that there would be an agreement for the government to last at least three Budgets, and that there would be "full parity of esteem" for Independents taking part.
Roscommon-Galway IA TD Michael Fitzmaurice told the Herald that agreeing a programme for government was more important that who got Cabinet posts.
He said if Independents are going to help people in their constituencies and the country as a whole, then a programme for government that should do that, not "Mercs and perks".
Asked if he would take a cabinet position if offered, he replied: "I don't know too many that would ever refuse it."