NAMA is "scouring" its portfolio to find possible social housing units at the request of the new minister Simon Coveney.
The agency's chairman Frank Daly and chief executive Brendan McDonagh have been quizzed by TDs from the Dail's housing and homelessness committee about what they can do to help solve the current crisis.
"We had a meeting yesterday with the Minister for Housing [Mr Coveney] which was very useful. He has encouraged us to look again at our portfolio to see whether we can find more for social housing.
"We have said we will do that and we are confident that we can come up with several hundred additional units which we will offer to the local authorities as soon as we possibly can."
Nama has committed to providing 20,000 residential units by 2020. Mr Daly said that Nama has previously offered local authorities 6,700 units for social housing but said they have been asked for just 2,500 of these.
Fine Gael's Fergus O'Dowd pointed out that in a number of cases local authorities which declined the most units are those that have the greatest demand, including the councils in Dublin.
He said it "makes no sense" and asked why it was happening.
Mr McDonagh said that one of the biggest issues was rules limiting the number of social housing units in any one area.
"The local authorities have an overall policy of approximately 20pc social housing and they generally do not want to go above that," he added.
"That's not acceptable," Mr O'Dowd replied.
"I agree with the Deputy," Mr McDonagh said. He said Nama asks their debtors to hold units back while waiting for an answer from local authorities. He said when they are turned down the properties are "snapped up in 24 hours" in the private rental sector.
Sinn Fein's Eoin O Broin, a former councillor in South Dublin County Council, said that "people seem to forget" the constraints put on local authorities by central government.
He gave the example of 591 units Nama offered to his former council with almost 500 of them in one location.