Meanwhile, in a leaked letter, Theresa May's hinted there could be customs checks in the Irish Sea in the event of no-deal with Brussels.
"The most important thing for me is the objective - and that is to give everyone in Northern Ireland and Ireland assurance that a hard border will not develop between north and south no matter what else may happen in the years ahead".
But she acknowledged that the "unique circumstances" of Northern Ireland "could require specific alignment solutions in some scenarios" on regulations.
May's plan would see the whole United Kingdom effectively agree to remain in the customs union to help avoid a hard border with Ireland as a backstop if no other arrangement can be found.
"There are stages to go through before it comes to Parliament", the DUP leader said.
Sammy Wilson, the representative of the party for Brexit, said: "From this letter it is clear that the government has decided on a plan reverse for Northern Ireland".
May's letter to the DUP said that she "could not accept there being any circumstances or conditions" for the Northern Ireland-only backstop coming into effect.More news: Circle this date: Dez Bryant faces Cowboys on November 29
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Arlene Foster says it has "raised alarm bells" as Mrs May appears "wedded to the idea of a border down the Irish Sea".
Writing in the Sunday Times, shadow Brexit secretary Sir Kier Starmer says he will work with other parties to stop a no-deal scenario.
The Democratic Unionist Party (DUP) interpreted a promise made by May in a letter that she would never let a division of the United Kingdom "to come into force" as an admission that such a clause would be included in a final deal, the Times reported.
The Prime Minister relies on the support of the DUP's 10 MPs for her Commons majority, votes which will be crucial as she attempts to get a deal through Parliament. It can not be watered down or bargained off.
Downing Street has played down suggestions that a Brexit deal is imminent, after the European council president, Donald Tusk, appeared to indicate a breakthrough could come within the next week.
His comments came on the same day Austrian newspapers reported that Brexit Secretary Dominic Raab and European Union chief negotiator Michel Barnier could meet over the next few days to seal an agreement.
Speaking at the British-Irish Council summit on the Isle of Man, Mr Varadkar said he was hopeful a Brexit deal could be done by the end of the year but it would not amount to a "clean break" as talks would have to continue.