Taoiseach Leo Varadkar has raised the prospect of the backstop, the insurance policy to avoid a hard border, applying only to Northern Ireland rather than to Britain as a whole.
However, Mr Varadkar said the Brexit withdrawal agreement, which spells out how the backstop would apply, would not be changed.
The backstop means the entire UK would remain in a common customs area with the EU, with add-ons in customs and regulations for Northern Ireland to keep the Border open, unless and until a future EU-UK trade deal that avoids a hard border is reached.
It was initially framed to apply to Northern Ireland only, but was later expanded to take in the entire UK because of British government demands.
Mr Varadkar said returning to this idea was a possible way to resolve the current Brexit impasse in an interview with RTÉ radio's Sean O'Rourke.
The withdrawal agreement has been repeatedly rejected by the House of Commons. Boris Johnson and Jeremy Hunt, the contenders to succeed Theresa May as British prime minister and Conservative leader, have said they want the backstop removed from the withdrawal agreement. The EU has said the withdrawal agreement will not be reopened.
Mr Varadkar said the UK could stay in the EU, or stay in the European single market and customs union, while also raising the Northern Ireland-only backstop.
"There is a possibility of having a backstop that applies to Northern Ireland and not to Great Britain, and that was previously proposed and offered by the negotiating team," he said. "That gets away from this idea that there is a great European plot to tie Great Britain to the orbit of Europe. "
The detail of the backstop is spelled out in the withdrawal agreement, but Mr Varadkar later said any changes would be a matter for the political declaration, a much looser document.
The withdrawal agreement says: "Until the future relationship becomes applicable, a single customs territory between the Union and the United Kingdom shall be established ("the single customs territory"). Accordingly, Northern Ireland is in the same customs territory as Great Britain." Advocates of Brexit have said this prevents the UK striking trade deals with other countries around the world.
Political declaration
The political declaration says the EU and UK are determined “to replace the backstop solution on Northern Ireland by a subsequent agreement that establishes alternative arrangements for ensuring the absence of a hard border on the island of Ireland on a permanent footing”.
“It was the British government that decided that they wanted to have a UK-wide backstop,” Mr Varadkar said, adding a Northern Ireland-only backstop would not “ go down well with the DUP at all”.
The British government currently depends on the DUP for its Commons majority.
Mr Varadkar said: "The withdrawal agreement, including the backstop, wasn't something the European Union and Ireland imposed on the UK. It is something we co-designed with the UK government.
“What I am going to have to do is meet the new prime minster once he has taken up office, once he has appointed his new cabinet, his new Brexit secretary. Have detailed, meaningful engagement.”