The group's latest Locked Out of the Market report finds just 33 places available within the discretionary rate, which can exceed the regular payment by 50%.
In nine of the 16 areas surveyed, there was no accommodation available to rent through HAP.
Simon Executive Director Wayne Stanley said the rental market is to blame.
“Thirty-three properties across 16 areas, between three different household types, means that really we’re still at a functional zero,” he said.
“The issue here is really that the private rental market is no longer a sustainable option for people to exit homelessness.”
“Across all local authorities where they document the number of people exiting homelessness, whereas a couple of years ago, it would have been 60% would go into the private rental market, those numbers have really fallen off a cliff,” he said.
“It’s still well below what we would need for the private rental market to be a functioning exit for people to leave homelessness.”
Housing Minister Darragh O’Brien has previously said the solution to rising homelessness is building more housing, which he said there has been a “significant increase” of in recent years.
Main image: Housing in Dublin.