A Brexit breakthrough is on the cards after British Prime Minister Boris Johnson ceded ground in talks on how to avoid a hard Border on the island of Ireland.
The potential deal, which has not got EU approval, could remove the need for significant customs checks on the island of Ireland.
Instead the heavier checks would be moved to ports and airports, effectively creating a border in the Irish Sea.
The move was discussed during a three-hour meeting after which the two leaders said they "see a pathway to a deal".
Mr Varadkar yesterday tossed aside the long-standing position that Ireland would not negotiate directly with the UK on Brexit.
Much of the meeting at a wedding venue in the Wirral was one-on-one before the Taoiseach and Mr Johnson were joined by officials.
The Irish side were providing updates to the EU taskforce in Brussels as the day wore on.
At one point the prime minister drafted in senior officials from the UK's Revenue and Customs service late on in the talks at Thornton Manor.
Both sides agreed not to reveal the detail of their talks publicly until it has been assessed by the EU's chief negotiator Michel Barnier and his team.
However, amid renewed hope that a deal can be secured in time for a UK exit on October 31, Tanaiste Simon Coveney said: "Mark my words, we are not there yet." And a DUP source told the Herald that Mr Varadkar had "over-egged" the outcome of the meeting.
The Taoiseach "can't be getting what he wants on customs as Boris loses his majority for a deal the second he does", the source said.
Mr Johnson's original offer last week would have seen Northern Ireland remain aligned to EU regulatory rules but outside the customs unions.
This was rejected by the Irish Government on the grounds that it would require tariffs and in turn checks on goods crossing between the North and the Republic.
The latest development could see the UK agree to a special 'treaty', which sources described as "a semi-free trade agreement".
It could involve Northern Ireland formally leaving the customs union but agreeing to follow its rules for a period.
The arrangement would have to be given some form of consent by the people of Northern Ireland.
Speaking in Liverpool after his meeting, Mr Varadkar was giving little away but said he believes it is possible "to have a treaty agreed, to allow the UK to leave the EU in an orderly fashion and to have that done by the end of October".
"But there's many a slip between cup and lip and lots of things that are not in my control," he cautioned.
When asked about who made concessions to break the impasse, the Taoiseach said: "I don't think this should be seen in the context of who's making concessions, or who the winners and losers are, I don't think that's the game any of us want to play."
On foot of the optimism, the pound made its biggest jump against the dollar in almost a year as investors seized on hopes of last-ditch progress.
Fianna Fail leader Micheal Martin said he was "pleased that the megaphone diplomacy has been replaced by proper and serious Brexit discussion today. The signals coming from Liverpool are encouraging and we hope that positive momentum can be sustained."
However, one European Commission source close to the Brexit process played down the positivity emerging from the Merseyside summit, saying early indications were that it "seems to be based on mood music rather than meat".
EU negotiator Michel Barnier will make a decision today on whether to restart formal talks with the UK's Brexit negotiating team following a meeting with Brexit Secretary Steve Barclay.