A number of groups say if the private sector find it too expensive to build – then the state should take over.
A housing executive would be able to borrow on lower interest rates than private companies can.
It comes as the latest DAFT report shows a severe lack of rental homes while Tipperary rents were on average 4.2% higher in the first three months of 2016 than last year with the average advertised rent now at €629, up 11% from their lowest point in 2013.
Economist David McWilliams says the state could build and rent homes relatively cheaply.