Asylum seekers would be obliged to contribute between 10% and 40% of their weekly income towards their State accommodation costs, under a plan to be considered by the Cabinet tomorrow.
Under the proposals, a person with a weekly income of up to €150 would have a potential contribution of €15; whereas a person earning up to €340 a week would be eligible to contribute around €83; and a person on €600 a week or more would contribute €238.
It is expected the new model, if approved by ministers, could be operational by next year.
Figures compiled by the Department of Justice last year suggest that around 7,600 people in the IPAS system would have been eligible to pay a contribution charge.
However, it is anticipated that number will likely fall once the EU Migration and Asylum Pact becomes operational next June, as it is expected to result in a fall in the numbers seeking asylum.
This is one of three measures being brought before the Cabinet tomorrow.
The other two relate to tightening rules around family reunification and increasing the residency requirement for citizenship from three to five years.
"That's in essence, what is envisaged by these reforms," he said.
Mr Martin said the reforms had come before the party leaders and also before the Cabinet sub-committee.
However the Irish Refugee Council warned that the proposed changes are "deeply alarming".
"They severely undercut two key pillars of refugee integration: a clear route to citizenship and the ability to reunite with family," it said.