A letter from the Minister for Integration to Cabinet colleagues more than a week ago, urgently seeking buildings to accommodate refugees, has so far failed to result in any formal offers, according to a department spokesperson.
Roderic O'Gorman asked for large halls to facilitate camp beds, mattresses and sleeping bags.
A number of departments have indicated that they are still searching within their portfolios to see if any buildings would be suitable.
In his letter to Cabinet colleagues, the minister said that he was urgently seeking any large buildings that could accommodate more than 50 people.
The aim was to create enough space to avoid situations where people were left without accommodation.
However, a spokesperson has confirmed to RTÉ's The Week in Politics that no formal offers of accommodation have been received since the letter was sent.
The State is currently accommodating more than 76,000 refugees.
Some departments have said that they are still searching within their portfolios for suitable buildings.
Meanwhile, the Dáil's Business Committee is considering the establishment of a new cross-party Oireachtas committee or informal caucus, to focus on migration.
Before Christmas then Taoiseach Mícheál Martin said that he would be open to such an idea.
The Department of Integration has also confirmed that it would be willing to engage with either body.
We will not turn away anyone - Varadkar
Speaking on RTÉ's This Week, Taoiseach Leo Varadkar said Ireland, like every other country in the European Union, is seeing an increase in migration.
Mr Varadkar said they need to be fair to those who need protection and they will not turn anyone away.
He said they have provided tens of thousands of people over the last year with shelter, education and healthcare, and he is "very proud" of that.
The Fine Gael leader said there are legal pathways to Ireland and 40,000 work permits were issued last year, but he added that they need to be firm with those whose applications are rejected.
"We need to say to people that if they're going to come to Ireland with a false story or under false pretenses, we will try to prevent you from entering in the first place," he said.
"After that, we will make sure your application is dealt with quickly. Due process is alway required, but we would aim to have applications dealt with in less than 12 weeks."
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Mr Varadkar said over 700 deportation orders were issued in the last month, although they do not know for certain how many people have actually left because many people "self deport".
They often have difficulty getting other countries to accept their nationals back, he added.
The Taoiseach said that while he believes people in Ireland understand that migration has been "a good thing for our country", they also want to know that it is going to be properly managed with controls.
"In the future I think we'll be proud of this country as to what we've managed to do," he said.
"We've taken in more Ukrainians per head than any other country in western Europe and by and large have been able to provide people with the protection that they need.
"In terms of finding additional accommodation, we're pulling out all the stops."
In relation to Minister Roderic O'Gorman's letter, Mr Varadkar said the Department of Justice has offered Thornton Hall, the Department of Education has offered student accommodation during the summer, and the Department of Enterprise, Trade and Employment has offered a former office building that is no longer needed.
The HSE has also offered a number of buildings that are currently being examined, he added.
"Some will available be in weeks, others will take months," he said. "A lot of these buildings are not in good condition and do need to be refurbished and that can take time."
Harris backs ministerial colleague
Minister for Higher Education and Justice Simon Harris said Roderic O'Gorman is "doing an excellent job" and has the "full support" of the Government parties.
Speaking on RTÉ's The Week in Politics, Minister Harris said they cannot reduce the Government and society's response to one letter.
"This is one letter and one moment in time," he said.
"We have managed as a country to accommodate more than 70,000 people. That has clearly required everybody stepping up to the plate - the people of this country and State agencies, and there's a lot more that we're going to do."
He also said that 964 fines were given by gardaí to airlines last year over a failure to properly check passenger documents. The maximum fine for the offence is €1,500.
Speaking on the same programme, Sinn Féin TD Pearse Doherty said it seems that this has been "left up to one minister" and "an all of Government approach" is needed.
He said a "coherent, comprehensive plan" needs to be communicated with local communities so that people are aware of what is happening and where it is happening.
Labour leader Ivana Bacik said a "fair and effective" immigration and migration system is needed and that Ireland has shown "a real welcome" to those fleeing conflict.
She said there is a need to debunk myths being perpetrated by a small minority of people.
