But Brussels appears set to insist on a Northern Ireland-only "backstop to the backstop" in case negotiations on a wider United Kingdom approach break down or any time limit on it expires.
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.
"I do think, when it comes to Northern Ireland, it's very important to listen to what the DUP has to say", the Taoiseach said.
He said the two sides were discussing how to avoid a hard border between Ireland and Northern Ireland.
But she acknowledged that the "unique circumstances" of Northern Ireland "could require specific alignment solutions in some scenarios" on regulations.
The DUP said it is "totally unacceptable that there could be a Withdrawal Agreement which provided that Northern Ireland at any time in the future could be subject to the rules of the Customs Union or parts of the Single Market whilst the rest of the United Kingdom was not".
Mr Varadkar went on to say that his objective on trade was to "avoid the emergence of any new borders".More news: Moeen bowls England to big win over SL
In the five-page letter to Arlene Foster, the DUP leader, and Nigel Dodds, her deputy, Mrs May said the European Union is still pushing for the "backstop to the backstop" but insists that she would never allow a divide between Ulster and Great Britain to "come into force".
One of the scenarios being discussed is Britain remaining in a customs agreement with the European Union for a limited period even after the end of the transition period on December 31, 2020, which would avoid the introduction of new border controls between Ireland and Northern Ireland, Walker said.
Speaking on the same programme, the DUP's Brexit spokesman Sammy Wilson said that the party's understanding of May's negotiating position represented a betrayal. However, she did not rule out the backstop being signed into the Brexit deal.
The response of the DUP has caused frustration in Downing Street, with sources insisting that Mrs May was not hiding behind "weasel words" and had stressed that she would not accept a deal which saw Northern Ireland hived off.
Prime Minister May already has a challenge on her hands in getting a Brexit Withdrawal Agreement through Westminster this winter with a majority of Labour MPs and some Conservatives set to vote against it.
In an interview with the BBC, Mrs Foster was asked did she trust the Prime Minister.
Toaiseach Leo Varadkar told a meeting of British and Irish officials on the Isle of Man that while negotiations were still at a "sensitive point", he was hopeful an agreement could be struck in the coming weeks.