EU member states will refuse to accept a Border that allows Ireland to be "an open gate without any control".
An EU source told the Irish Independent that all other member states will insist on sufficient border controls and will take a hardline on protecting the internal market from smuggling.
The prime concern is preventing unauthorised goods and people getting into EU territory.
They must ensure "Ireland is not an open gate without any control - the EU will not accept that", said the source.
By far the most difficult problem with Brexit is arriving at a solution to the Irish Border.
Despite a series of fractious discussions last week among members of the British government's special Brexit committee - also known as the Brexit war cabinet - no solution to the conundrum on the Border was forthcoming.
The talks also failed to yield an outline of how the UK sees its future relationship with Europe. Instead, UK Prime Minister Theresa May reaffirmed her country's stated red lines that it will leave the customs union and single market.
"It is by far Britain's biggest problem, because it is impossible to maintain the status quo on the Border and stay out of the customs union," said the EU official.
The Irish issue is about to consume "an appalling amount of time during the talks", it is the one issue that could 'thwart' the whole process, they added.
The EU's lead Brexit negotiator Michel Barnier last week also confirmed a Border was "unavoidable" if Britain stays outside the customs union.
Britain leaving the customs union immediately demands customs checks will be required between Ireland and the UK.
The option of having a border between the island of Ireland and Britain is also not an alternative option on the insistence of the DUP - Theresa May's coalition partner.
In this case, the Irish State will be obliged to apply tariffs on goods coming from the UK as Britain will no longer have access to the EU's tariff-free customs arrangements.
So far London has claimed that a series of technical solutions such as cameras and special registration will ensure the Border remains frictionless.
But UK officials have yet to be specific about exactly how they will work, or whether they will satisfy what is required.
Irish officials have dismissed this as "magical thinking".
Meanwhile, the Taoiseach has issued several warnings to Downing Street, saying time is running out.
Britain is supposed to exit Europe by March 2019. According to the EU-UK timeline, the terms of the transitional period are supposed to be signed off by March 2019.
This is the implementation space for Britain to put its Brexit deal in place.
Hard Brexiteers were vocally exercised about the terms of the transition period, because they demand the UK adheres to all EU rules and regulations for as long as it lasts.
British-government commissioned reports released last week illustrated the gloomy and foreboding impact of Brexit on the economy if talks fail. In spite of these foreboding realities, the delay in agreeing transition and the hold up on the Border do not inspire confidence in the road ahead.