A Dexeu spokesman said the reports were "completely false", adding: "A significant amount of work and decision-making has gone into our no-deal plans, especially where it relates to ports, and we know that none of this would come to pass".
"Once again this shows the lack of knowledge of border areas and the concerns they face", Anderson said.
Under the EU proposal, if all other attempts to avoid a hard border fail, Northern Ireland would form a "common regulatory area" with the bloc, in effect keeping the British province in a customs union with the EU.
They said: "We are entirely dependent on Europe reciprocating our posture that we will do nothing to impede the flow of goods into the UK".More news: Priyanka Chopra & Nick Jonas Enjoy a Dinner Date in L.A.
A Downing Street spokesman said: "The Prime Minister has been absolutely clear that we can not and will not accept a customs border down the Irish Sea, and that we will preserve the integrity of the UK's common market".
"To suggest that Northern Ireland be tied to both EU and UK regulations, when one of the objectives of leaving the [EU] Single Market is to allow the UK to set its own regulations, raises the question which regulations apply to Northern Ireland if and when the UK and the EU regulations diverge", he said. That would likely require Northern Ireland to retain some European Union rules.
"The UK Government must urgently clarify its position and guarantee that Scotland will not lose out".
The special economic zone will mean traders, who constitute 90% of cross-border traffic, can operate under the same rules as those south of the border, the report said, citing a senior government official.
However, finding a practical solution for any customs checks needed after Brexit has proved elusive.More news: Dog found dead in cargo hold on Delta Air Lines flight
John McGrane, the Director-General of the British Irish Chamber of Commerce, dismissed the proposal and said it was too late to be floating "vague, unworkable" ideas.
May previously pledged to take the United Kingdom out of the EU customs union by considering two options.
There was no immediate response from the Department for Exiting the European Union to a report in the Sun suggesting the Brexit secretary was to put forward a radical solution to the thorny issue of future customs arrangements.
The three scenarios include a mild scenario, a severe one and, finally, "armageddon", according to the Sunday Times.More news: Microsoft in Talks to Buy GitHub