A Northern Ireland Executive and assembly could be retained in a united Ireland, the taoiseach has said.
Micheál Martin said support would be provided from Dublin in "external matters", with British government input also.
He said it would be a three-way relationship.
Meanwhile, a poll suggests a majority on both sides of the border want an NHS-style health system in a united Ireland.
In Northern Ireland, 82% of people agreed that Ireland should adopt a British-style health care system with no charges for prescriptions or A&E and GP visits.
In the Republic of Ireland, 70% of people agreed with the proposition.
The poll was commissioned by BBC NI's Spotlight programme and these results were revealed on The View on Thursday night.
The poll also suggests that:
- 46% of people in Northern Ireland and 21% of people in the Republic believe Ireland should change the design of its flag to accommodate unionist sentiments in a united Ireland
- 57% of people in Northern Ireland believe the Republic should change its national anthem to one that is "more inclusive", compared to 38% in the south
- 40% in Northern Ireland believe the executive and assembly should be retained under the authority of Dublin, compared with 42% in the Republic
In an interview with former BBC News NI political editor Mark Devenport for Spotlight, Mr Martin said he believed the latter point could be a possibility.
"You could have still a northern assembly and the northern executive, potentially, with the fulcrum towards Dublin, in terms of external matters and so on," Mr Martin said.
"But the British government would still be involved."
He added that the "three sets of relationships have to be at the cornerstone".
Findings of the same poll released earlier this week found that a majority of people on both sides of the Irish border believes Northern Ireland will have left the UK within 25 years.
Most respondents said they thought NI would still be part of the UK in 10 years time, but not in 25 years.
The poll was carried out by the NI Pollsters LucidTalk and the Irish polling firm Ireland Thinks.
- In Northern Ireland polling was carried out online between 5 and 7 April and 2,845 responses were used for the analysis
- In the Republic of Ireland polling took place between 6 and 9 April and 1,088 responses were analysed. A small amount of fieldwork was carried out in the Republic of Ireland on 10 April.
The margin of error is +/- 2.5%.