The Government is considering an opinion from its legal advisers which suggests that the constitutional right to Irish citizenship for all children born on the island of Ireland should be withdrawn.
While a referendum would be required to change the Constitution, the Government has not yet taken any decision on the matter.
However, a senior political source said yesterday that the debate within the Government was now moving away from the referendum option.
The legal advice is being considered against the backdrop of a Supreme Court ruling last year which said that the non-national parents of an Irish-born child cannot, as a matter of course, claim the right to live in Ireland.
That judgment has not had the effect of stopping non-national women from presenting late in their pregnancies to give birth at Irish maternity hospitals.
While parents are no longer automatically entitled to live in the State, their children still retain the automatic right to Irish citizenship and, therefore, an EU passport.
The Government's legal advice suggests that a referendum should be held to remove the automatic right to Irish citizenship.
It is believed to state that this would remove an incentive to give birth in Ireland.
The advice is also believed to refer to political pressure from other EU member-states which are concerned that Irish-born children will exercise their right to live anywhere in the European Union.
While a spokesman for the Minister for Justice, Mr McDowell, would not discuss any aspect of the legal advice under consideration, he said no policy decision had been taken on the matter yet.
Sources said the most significant factor to have emerged in the debate was the clause in the Belfast Agreement which gave people born in Northern Ireland the right to Irish citizenship.
This was incorporated into the Constitution after the referendum in June 1998 which gave effect to the agreement.
Sources said there was a reluctance at senior levels in the Government to tamper with the agreement, given the Government's political commitment to it.
Before the referendum, Article 2 said that "the national territory consists of the whole island of Ireland, its islands and the territorial seas".
The Belfast Agreement replaced this article with a clause stating that "it is the entitlement and birthright of every person born in the island of Ireland, which includes its islands and seas, to be part of the Irish nation".
It adds: "That is also the entitlement of all persons otherwise qualified in accordance with law to be citizens of Ireland.
"Furthermore, the Irish nation cherishes its special affinity with people of Irish ancestry living abroad who share its cultural identity and heritage."