The Tánaiste confirmed this afternoon that the Government has asked the Attorney General to investigate the implications of the findings in today's preliminary Census report.
The figures show that a number of constituencies are over quota for TD representation while some are under-represented.
This could require an increase or a decrease in seats in certain constituencies.
Under the constitution there should be one TD for every 20,000 to 30,000 people.
Initial results from this year's census show the population has grown to 4.2 million.
It is the fastest annual growth rate in population of the EU over the last decade, at 1.6%.