Thirty-nine Direct Provision Centres across the country are full.
The Irish Examiner reports that in five counties there are at least 100 asylum seekers in emergency accommodation.
In Dublin, over 400 are in temporary housing, while there are 209 in Monaghan.
Last week the Government reduced plans for a facility in Ballinamore in Co. Leitrim to 27 places after locals protested the volume of people coming into the area.
Seven families will be moved into apartments in the Leitrim town next month - which a community group has welcomed saying the plan is more sensible.
"We welcome the fact that the Minister is facilitating the fact that it will be families to live and work amongst us. Ballinamore has never said no to housing asylum seekers, it has always been about working with the community," said Gordon Hughes from Ballinamore Community Group.
A spokesperson has been quoted in reports this morning saying they are determined to ensure people coming to Ireland seeking protection have accommodation.