The Coalition leaders are meeting in Dublin and are expected to sign off on a further tightening of migration rules, relating to the criteria for family reunifications.
The proposals have been brought forward by Minister for Justice Jim O'Callaghan and Minister of State Colm Brophy.
If passed by Cabinet next week, it will likely result in a reduction in the total number arriving under the family reunification policy which stood at 22,000 last year.
Applicants seeking family reunification will also have to be self sufficient and not owe accommodation costs.
Separately, the Coalition leaders are also discussing plans to change the current requirement that people who are granted refugee status may apply for naturalisation after three years' resident.
The new proposal would increase that to five years.
It comes as Minister O'Callaghan said earlier that Ireland will need to be "nimble" and may need to change its own laws and provisions in order to respond to a proposed overhaul in UK asylum laws.
Britain is set to overhaul its approach to human rights' laws to make it easier to deport migrants who arrive illegally, in a major shake-up of asylum policy.
Mr O'Callaghan said he expects the proposed changes to UK asylum laws will have an impact on Ireland and that the Government may have to change the law here in response.
In a statement this evening, the minister said he and the Government are aware that changes to the UK's asylum practices or laws can result in changes to the flow of asylum seekers between the UK and Ireland.
"I am committed to ensuring that Ireland is not viewed more favourably than the UK by those seeking to claim asylum," he said.
Mr O'Callaghan said he will closely monitor the changes proposed by the UK government and will "respond to those proposals having considered them fully and discussed them with Government colleagues".
"I will be publishing a new International Protection Bill to reform Ireland's asylum system later this year and any necessary changes arising from the UK’s change of policy can be included in that Bill," he said.
"Prior to the changes proposed by Home Secretary Mahmood, I had already directed a separate review of Ireland's rules on family reunification and will shortly bring proposals to Government in respect of this issue."
The minister also spoke earlier at Farmleigh House following the British Irish-Intergovernmental Conference where he and Tánaiste Simon Harris met British Secretary of State for Northern Ireland Hilary Benn and Under-Secretary of State for Northern Ireland Matthew Patrick.
Mr O'Callaghan said "every country has a right to introduce its own migration policy".
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"The British government has every right to bring forward its own proposals, but we would ask and are grateful for close engagement, because we clearly have interdependencies here because of the contract here," he said.
The minister stressed that changes to the UK asylum laws "can have an impact in Ireland" and "have had an impact in the past".
"But that's not to say that the UK can't change their asylum laws. They're perfectly entitled to change their asylum laws, and I thank them again for giving us a heads up in respect of it, however, what it does indicate is that I suppose we need to be nimble in Ireland as we may need to change our laws and our provisions as well to respond to any changes that have taken place in the UK," he said.
Read more: UK to cut refugee protections under asylum 'overhaul'
Mr Benn said he did not believe any of the new proposals would put the UK at odds with its obligations under the European Convention on Human Rights.
"The British government is absolutely committed to the European Convention of Human Rights, unlike other parties in Britain who want to take us out of it, and that really would undermine the Good Friday Agreement, which has seen so much progress take place in Northern Ireland," he said.
Mr Benn said there is a debate going on in the Council of Europe about the interpretation and application of various aspects of the ECHR, adding that "there is a great deal of public concern about illegal migration to the United Kingdom".
"This is undoubtedly the case, and that's why it's vital we have a system that everyone can have confidence in, that can distinguish between those who are trying to move for other reasons by claiming asylum, when, in fact, the sovereign system is there for people who are fleeing persecution," Mr Benn said.
