Two political parties are calling for a total ban on all rent increases for the next two to three years.
The Taoiseach says the idea, put forward by The Social Democrats and Sinn Féin, "probably wouldn't work".
Social Democrats TD, Roisin Shortall, suggested it would be policed by renters self-reporting cases where landlords try to hike prices.
"There should be a blanket freeze on rent at this point, to stop spiralling rents".
She said current measures in place to help make renting more affordable "are clearly not working".
Deputy Shorthall believes there is "no other measure" other than freezing all rents that will help tenants until the housing supply increases.
Under current rules, landlords can only increase rents by 4% a year, however there are ways to get around the rent cap.
Landlords are allowed to raise rents by more than 4% if they carry out "extensive renovations" on a home, but there is no clear definition for what type of works apply.
There is also concern that when a tenancy ends, homes are being advertised to rent for a significantly higher price than had last been paid.