According to the report which analysed trends during July, August and September the average monthly rent in Limerick city is now €946 while a property in County Limerick will set you back €748.
In Dublin, the Daft.ie report shows the increase in rents in the year to September was 12.3% and rents in the capital are now nearly 23% higher than their previous peak in 2008.
Cork experienced a jump of over 5%, Galway, 9.8% and Limerick rose by 10.9%.
Galway Bay fm newsroom - House rents in the city are up nearly 10 per cent since previous year.
Prof Lyons said the rental figures did not make happy reading, adding: "Extra supply is quite simply the only solution".
He said: "There isn't a single part of the country where rents are increasing less than 4% a year which is what the rent presure zones are created to do".
Mr Allen added that the housing market was witnessing "a collision of different forces" - a view bolstered by another report, published today by the Economic and Social Research Institute which suggests house prices could rise by 20% over the next three years.
"It is not clear to me that the system of rent pressure zones is working, in fact it may be having the opposite effect".
However, he said pressure zones were not being adhered to by some landlords and a transparent rent register should be considered.
He said: "There were just under 3,400 properties available to rent nationwide, that's for the entire country".