A first-time buyers' grant, expected to be announced in Budget 2017 next week, may apply to new builds up to the value of €400,000, it is understood.
A rate of 5% is being considered.
A senior source yesterday said the maximum refund paid to first-time buyers would be €20,000.
The Cabinet this evening held its last meeting ahead of next Tuesday's Budget.
The Independent Alliance met the Taoiseach and Minister for Finance Michael Noonan and Minister for Public Expenditure and Reform Paschal Donohoe today about the Budget.
Fianna Fáil's Dara Calleary also met Minister Donohoe today and further contact is due tomorrow.
A significant amount of discussion has yet to take place ahead of the Budget, according to Minister Donohoe.
He said this morning he remains confident the Budget will pass next week.
Speaking in Dublin, Mr Donohoe said he believed it would be "fair for Ireland and would make significant progress towards addressing the many challenges and opportunities facing families" across Ireland.
Asked if it was being shaped entirely by Fianna Fáil, the minister said Government had to frame Budget 2017 in a "new political context" which included commitments made in the framework for government with the "main Opposition party".
He said that not all of these targets or any targets would be achieved in one budget but across a number of budgets.
Asked about childcare and suggestions of cuts to the Universal Social Charge, Mr Donohoe said he could not comment on specifics that would be included in the Budget announcement on Tuesday.
In relation to public sector pay, Mr Donohoe said there were a "variety" of public sector wage issues, but the Lansdowne Road Agreement remained in place and in many sectors the agreement had delivered for those still inside it, such as the INTO.
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Meanwhile, Minister for Social Protection Leo Varadkar has indicated that he will be prioritising other welfare payments besides the State pension in next week's Budget.
Mr Varadkar said if there was an increase for pensioners in the Budget, other groups will have to benefit as well.
Those groups included carers, widows under the age of 66, people in receipt of illness payments, and families who have children in poverty.
The minister said it was important that the Budget passes the fairness test and those categories accounted for somewhere between 400,000 and 800,000 people.
Later in the Dáil he was pressed by Independents4Change TD Joan Collins for a commitment that the mooted €5 weekly increase in the State pension will be announced in Tuesday's Budget.
Mr Varadkar said he had never given the €5 figure "and I can't because it is not agreed yet".
Separately, Minister for Communications Denis Naughten has said he will putting the case for funding necessary for the revitalisation of rural Ireland to the Minister Donohoe.
He said within his own department he will be prioritising the issue of energy efficiency.
Mr Naughten said relations between Independent and Fine Gael ministers have been good in the negotiations on the Budget.