Mr Varadkar's comments came after a leaked letter from Theresa May to the Democratic Unionist Party suggested a border down the Irish Sea could be included in the withdrawal agreement.
A Brexit deal is now being thrashed out in Brussels amid talk of a final agreement in the next week.
It led to the DUP's Brexit spokesman Sammy Wilson to accuse the Prime Minister of being guilty of a "total betrayal" of her promises that Northern Ireland would not be treated differently from the United Kingdom should Downing Street and Brussels fail to secure a future trade deal.
In it, Ms. May reportedly tried to assure her allies that she would never allow a Brexit deal proposal offered by Brussels to "come into force".
The British prime minister wants a "backstop" measure which would create a temporary "joint customs territory" with the European Union for the whole of the UK.
'The PM's letter raises alarm bells for those who value the integrity of our precious union & for those who want a proper Brexit for the whole UK, ' DUP leader Arlene Foster tweeted.
This backstop - created to avoid a hard border on the island of Ireland - would be the last resort option and come into effect only if future trade negotiations failed to produce a solution for preserving the open Irish border.
The Taoiseach said "I'm hopeful it can be done in the next few weeks".
The Northern Irish party which props up Prime Minister Theresa May's government on Friday cast her Brexit negotiation as a betrayal and cautioned it could not support a deal that divided the United Kingdom.
The scope of any alignment with Brussels' rules would be limited to what is "strictly necessary" to avoid a hard border.
"And I think if we do that, if we listen to the voice of Northern Ireland as a whole that will help us to come to an agreement".
However, in the leaked letter, it is revealed Mrs May admitted to the DUP that the European Union is still proposing a Northern Ireland-only backstop arrangement alongside a UK-wide solution.
May will meet Belgian Prime Minister Charles Michel this morning before heading to France where she will meet President Emmanuel Macron, who is one of EU's the most hardline leaders when it comes to Brexit.
The issue is dominating a meeting of the British Irish Council in the Isle Of Man today.
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.
"I hope and I believe that we can secure that majority in Parliament for the agreement".
"Even when all of that is done, then we begin the talks on the future relationship", he added.
"Brexit is going to go on for a very long period of time".