May is expected to brief the Cabinet on progress in talks when members gather for their weekly meeting at 10 Downing Street on Tuesday.
Plan removes the need for a so-called "backstop" on the Northern Irish border issue.
But the customs deal created would be "a customs union" - a bespoke option created specifically for Brexit - rather than "the customs union", or continued membership of the structure that already exists.
"Brexit has undermined the Good Friday Agreement" - the 1998 peace deal that ended three decades of violence in Northern Ireland - "and it is fraying relationships between Britain and Ireland", Varadkar said.
Ireland's prime minister has told Theresa May in a hastily arranged phone call that he cannot allow the United Kingdom to unilaterally decide when to terminate the Irish backstop, creating the possibility that Britain could be tied in a customs union with the EU for the long term.
At the same time, it reported that the prime minister was on course to agree a future economic partnership that would leave open the possibility of Canada-style free trade deal sought by Brexiteers.
"Negotiations are still very firmly continuing, and therefore we are 95% of the way there in relation to the Withdrawal Agreement".
He said: "The prime minister has been clear that we are making good progress on the future relationship and 95% of the withdrawal agreement is now settled and negotiations are ongoing".
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They are reported to include U.S. allies India, Italy, Japan and South Korea . "Hundreds of businesses have departed Iran", he said.
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Taylor, 39, took an unprecedented one-year leave of absence from his post as mayor for his deployment to Afghanistan in January. Taylor leaves behind a wife and seven children, according to the Deseret News of Salt Lake City.
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He scores important goals, makes important challenges, is a good passer of the ball and nearly always completes 90 minutes. After City, after Chelsea, maybe today we are more near in our performance to be in front of them. "It was very intense.
A Downing Street spokeswoman added: "The prime minister is clear we are leaving the customs union".
Ireland and the European Union will "never" accept a time-limited Brexit backstop, the United Kingdom has been told.
A No10 spokesman said the British and Irish leaders had agreed the backstop would "a temporary arrangement", but May had emphasised that there would need to be "a mechanism through which the backstop could be brought to an end".
"This has been committed to by the United Kingdom in order to have a withdrawal agreement".
"If the long term is that we are simply going to be continuing this argument long after we've left the European Union on March 29 next year as to what our future relationship with it is going to be, then, quite frankly, it would be better to have that argument now and let the public decide what they want and if they are content with the arrangements the government has come up with".
Chief Executives from Waterstones, Innocent Drinks and Lastminute.com stated that the United Kingdom faces either a "blindfold or a destructive hard Brexit" in the note.
Other people who put their name to the letter include Cobra Beer founder Lord Bilimoria, former Marks and Spencer chairman and ex-Labour peer Lord Myners, Alex Chesterman, founder of the Zoopla property website, and Sir Simon Robertson, the ex-chairman of Rolls-Royce.