The UK is due to leave the European Union at 23:00 GMT on 31 October. Even if, as United Kingdom officials hope, Brussels shows flexibility on the timeline, they have yet to enter the "diplomatic tunnel" of final text negotiations.
The European Commission has confirmed that the EU and British teams "have agreed to intensify discussions over the coming day", but according to CNN reporter Bianca Nobilo this falls short of "secret tunnel talks", and is "more of a journey into Plato's cave".
Barnier's team has been in "technical talks" with British officials for some time, but these were not making enough progress towards a treaty text that could forestall a chaotic "no-deal" Brexit in three weeks.
Mrs Foster's statement comes after her party gave their backing to the Prime Minister's Brexit proposals last week, which would effectively see a border erected down the Irish Sea and keep Northern Ireland in the Single Market.
The EU's chief negotiator Michel Barnier is now meeting with Britain's Brexit minister Stephen Barclay in Brussels.
EU Council President Donald Tusk said he has "received promising signals" from Irish Prime Minister Leo Varadkar that a Brexit deal is still possible, so he has extended a deadline to continue the Brexit talks.
But he cautioned there could still be obstacles along the way in what has become a more than three-year game of high-stakes political snakes and ladders.
The pair are attempting to strike a deal before the proposed Brexit date of October 31.
Refuses to discuss what concessions he's offered European Union but... Since the 2016 British referendum vote for Brexit, negotiations have bounced back and forth between London and Brussels.
It noted that any deal must contain a "legally operative solution" that avoids a hard border on the island of Ireland while protecting the island's economy, the Good Friday peace accord and the EU's single market.
Johnson and Varadkar met at Thornton Manor, a venue more commonly used for luxury weddings than discussing global divorce terms.
Separately, two senior European Union diplomats told Reuters the possible solution could include two elements: keeping Northern Ireland inside the UK's customs regime while also carrying out any customs and regulatory checks together.
Northern Ireland's opt-in to the plan would be open to four-yearly review by the province's devolved assembly and executive.