"We will be setting forwards those proposals. Can I just explain why we are setting forward our own proposals? It is because the plan the European Union put forward is not acceptable to us. Because the plan the European Union has put forward is one that effectively keeps Northern Ireland in the customs union and ensures that effectively there is a customs border down the Irish sea," the PM said in an interview to BBC on Tuesday.
In response to May's statement, the Democratic Unionist Party (DUP) leadership is waiting to see "what the text actually says in relation to any offer that has been made to the European Union."
For the unionists in Belfast, however, the being separated from mainland Britain by a hard border is a no-go zone.
"It's been very clear all along. That has been our one red line — that we cannot have a customs border down in the Irish Sea or a regulated border because that would make us separate from the United Kingdom. That doesn't work from the constitutional prospective and it doesn't work from an economic prospective either," the DUP leader Arlene Foster said.
The ongoing Conservative Party conference in Birmingham has been reported as a breeding ground for a viable Brexit plan that would liberate her government, allowing it to start external trade negotiations.
The DUP are allegedly groomed to accept some increased forms of checks "in the Irish Sea" between Northern Ireland and Great Britain. A UK-wide alignment with relevant EU customs union rules will reportedly be provided if one of the "hybrid models" is confirmed by the government.
The DUP speak to the government on an ongoing basis and recognize that Britain is reaching a crunch time in Brexit negotiations, the DUP leader Arlene Foster admitted in an interview.
Meanwhile, the eurosceptic rebels in Britain's ruling party have come up with a solution to the issue north-south land border on the island of Ireland, a former junior Brexit minister said.
"We believe that we have produced a proposal which can operate within the current framework of technology and administration to deliver a free flowing border with no infrastructure on the island of Ireland within the boundaries of a free trade agreement," Steve Baker said on Tuesday.
Theresa May's Conservative Party has been in coalition with the DUP since the 2017 snap elections, making the government somewhat dependent on the Norther Irish party for a majority voice in the Parliament.