The Minister for Housing, Planning and Local Government has said the homeless figures for July are still being compiled, but he believes the numbers are up on the previous month.
Speaking on RTÉ's Today with Miriam, Eoghan Murphy said he cannot be certain if the number of homeless people will hit 10,000 but he said no matter the figure, the problem remains the same.
Figures for June from the Department of Housing showed more than 9,870 people were homeless.
Today, Mr Murphy said one-in-five houses built this year will be social houses, and that will remain the case for the next five years.
He said it is his responsibility to fix the problem and that is what he is focused on.
The minister said the root cause of the homeless crisis is a lack of supply.
He said the Government is going to hit the target of increasing the housing stock by 50,000 by 2021.
Mr Murphy said his department is reliant on local authorities to build social housing and some are building, some are not and others are facing significant delays.
The Labour Party's housing spokesperson Jan O'Sullivan has accused Mr Murphy of avoiding the realities of the housing crisis.
She said: "In the last month alone, we have seen families sleep in garda stations to avoid sleeping on the streets and protesters occupy buildings that have been lying vacant.
"Every month the homeless figures are rising and the numbers of children homeless are rising, this is not a sign that Rebuilding Ireland is working."
Ms O'Sullivan said a more urgent response was now needed from the State.