Mr Varadkar issued the warning after British negotiators tabled demands for an "escape clause" from any backstop deal, which would trigger a no-deal Brexit.
Prime Minister Theresa May will bring plans to avoid a hard Border to her divided cabinet tomorrow.
Sabine Weyand, the deputy to Michel Barnier, ...
May's deal, based on the Chequers plan which prompted Johnson and former Brexit Secretary David Davis to resign from her Cabinet, would see Britain agree to a "common rulebook" with the EU on goods and agri-products - identical to the EU rulebook, and interpreted by EU judges - and remain inside the bloc's Customs Union, as a so-called "backstop" solution to the vexed question of keeping the Irish border open.
They believe it would prevent Britain securing new free trade deals with other countries, and would break the Conservatives' manifesto promise to leave the customs union. "That is why we are increasingly positive on the expectation of reaching a deal", he said at a conference in London today.
The new deal will bring the United Kingdom closer to the prospect of a free trade deal with the European Union similar to that of Canada, it has been suggested. "Severe punishment at general election if this goes ahead". Appears any old deal now better than no deal'.
It is said that the Prime Minister hopes the agreement will placate remain-backing Tories and win over some Labour MPs.
A senior EU source said the United Kingdom prime minister would need determine whether she could sell an open-ended customs union to her party, but the calculation in Brussels was that it would be acceptable to the House of Commons as a whole.
The EU has reportedly accepted that customs checks can take place at shops and factories, rather than at the border - which, if true, would remove the problem of where to put the customs border post-Brexit.
"The EU will write an all-UK customs deal into the legally binding withdrawal agreement so an EU-designed "backstop" treating Northern Ireland differently from the United Kingdom mainland is not required", the Sunday Times said.
While European Council President Donald Tusk said in September that an extraordinary summit would be called for November 17-18 to finalize and formalize the EU-UK arrangement if sufficient progress in talks was reached, the EU leaders are now not planning this extraordinary summit.
Last night Downing Street sought to play down expectation that a customs union deal was close to being agreed.
Earlier on Monday, the Irish deputy prime minister, Simon Coveney, tweeted: "The Irish position remains consistent and v clear that a "time-limited backstop" or a backstop that could be ended by United Kingdom unilaterally would never be agreed to by IRE or EU".
A spokesman insisted: 'Nothing has been agreed'.