Ireland's foreign minister said no such proposal existed.
Varadkar rejected suggestions from some British pro-Brexit politicians that technological solutions such as the tagging of goods and vehicles and computerized customs declaration might allow trade to continue along a "frictionless border".
Dublin's attitude has reportedly hardened following the appointment of Leo Varadkar as prime minister and his selection of Simon Coveney as his minister for foreign affairs last month.
The MP for Lagan Valley said that the Irish Government was being "too pessimistic" in its approach to the border issue and should be "careful" in its inference that a border would lead the IRA back to violence.
Leo Varadkar wants customs and immigration checks at the country's post Brexit border with Britain
But Simon Coveney denied that the Irish government preferred that option.
With everything from the peace process to the current economic standing of the nation hung in the balance of the final outcome of the Brexit negotiations, there is still a long way to go before Varadkar and the rest of the Irish government will be done with the Ireland's part to play in the UK's future with the EU.
However, sources have told The Times that Mr Varadkar thinks these plans could jeopardise the peace process in Ireland and restrict movement between the two countries.
But chancellor Philip Hammond says that idea simply can't be accepted.
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The issue of the border between Northern Ireland, which is leaving the European Union, and the Republic of Ireland which is not, is one of the most contentious and complex issues around Brexit, made worse by the UK's commitment to leaving the customs union.
"The answer to how to deliver that can not be to create a border between Northern Ireland and Great Britain".
Before the Taoiseach's border plans came to light, the Irish Ambassador to the United Kingdom had told Sky News his country hoped the United Kingdom would reconsider exiting the single market and the customs union in order to swiftly dismiss talks about a hard border.
This resulted in Minister Farry telling a Stormont committee that "the government of Ireland are not fulfilling their duty to provide for the training and education of their young people, and we are, effectively, picking up the pieces".
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"It's as simple as this: between Ireland and Northern Ireland there is a political border. Dublin really needs to understand that the proposition is absurd, it's unconstitutional", DUP MP Jeffrey Donaldson told BBC Radio Friday.
"There is no way that the DUP would go for an option that put a border between one part of the United Kingdom and another".
Coveney reiterated that Britain could not pretend that they can solve the border problem through technical solutions such as putting cameras on the 400 road crossings along the frontier. "We can not support any proposals from the British or European side for the re-emergence of a border", he said.
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