The EU has suggested that a backstop post-Brexit customs arrangement covering all of the United Kingdom could give mainland Britain some scope to set trade rules while keeping the province of Northern Ireland aligned with the EU, European diplomats and officials said.
The backstop ensures that Northern Ireland would stay "aligned" to the regulations of the single market and the customs union if there is still no other solution that would avoid infrastructure along the Irish border.
But talks over Britain's withdrawal terms remain stuck due to a dispute over the Irish border, and the outlines of a potential deal taking shape look little like what the leave camp promised two years ago.
The plan sees the whole of Britain remaining in the EU customs union - not just Northern Ireland.
It mirrors the approach used by prime ministers of the recent past to make decisions during armed conflicts or incidents like foot and mouth, when normal cabinet committee processes are too cumbersome to keep pace with the demands of decision making.
"The Tanaiste couldn't have been clearer that a time-limited backstop or a backstop that could be ended by the United Kingdom unilaterally would never be agreed to by Ireland or the EU".
UK Brexit Secretary Dominic Raab.
Downing Street called the leaders' discussion a "constructive conversation", and said May and Varadkar had agreed that any backstop must be temporary.
A Downing Street spokesman said on Sunday the report was "speculation" and that negotiations with the European Union are ongoing, although he reiterated the government's line that the withdrawal agreement is 95 per cent complete and that it's making progress on the future relationship.
May told Varadkar that there would need to be a mechanism through which the backstop could be brought to an end, a spokesman from her office said in a statement.
The Taoiseach has said Brexit has undermined the Good Friday Agreement and is fraying relations between Ireland and Britain.
Justice Minister Charlie Flanagan said he wouldn't add to what he described as "speculation".
"He recalled the prior commitments made that the backstop must apply "unless and until" alternative arrangements are agreed".
Sinn Fein president Mary Lou McDonald has urged the Irish premier to stand firm over a proposed backstop plan to prevent a hard border in Ireland after Brexit. "I certainly hope we are".