But Foster refused to consider such a compromise on Tuesday, saying: "What we said to Barnier is checks of themselves are symptomatic of something different, so we only need checks if Northern Ireland is following a different regulatory regime to the rest of the UK".
With the negotiations coming to a head, the central focus of the discussions is thought to have been the issue of the Northern Ireland "backstop" meant to ensure there is not return of a "hard border" with the Republic.
According to one of the academics who conducted "The Future of England Study", unionists' preference for Brexit over the territorial integrity of the United Kingdom "raises questions about the type of union we're in, and indeed what unionism means".
"The whole point about checks is that there is a difference" she said.
The UK Government has promised to set out further proposals on the "backstop" arrangement aimed at avoiding a hard border with Ireland, with speculation that it could involve regulatory checks on goods travelling between Britain and Northern Ireland.
Labour has indicated it will oppose a deal based on the Prime Minister's Chequers plan and will push for a general election or, possibly, a second referendum.
The UK Government is also due to publish its own revised proposals for the Irish border, but Downing Street has said only that these will appear "in due course".
The discussion is expected to include a commitment to keep the whole of the United Kingdom in an effective customs union with the EU after Brexit, but with a "clear process" of steps to exit.
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The spectacle was astounding simply because it might be the first time Trump was silenced by someone else's inchoate ranting. West called the president's work on criminal justice reform (an issue close to wife Kim Kardashian's heart) "bravery".
Theresa May has urged MPs across the Commons to act in the national interest and back a Brexit deal amid warnings that "decisive" progress is needed in the negotiations before a crunch Brussels summit next week.
Ahead of an upcoming European summit next week, the UK Prime Minister held a meeting with members of the Brexit "war cabinet" on Thursday to seek support for the newly proposed terms of the withdrawal agreement and prevent any potential resignations over her backstop plan.
But he said a "Canada-plus-plus-plus" deal was "within our grasp with political will and imagination".
However, May has not yet shown the new proposal to Foster, whose party the prime minister depends upon for her Commons majority.
According to the BBC, Brexiteers were particularly concerned over the fact that Britain could be tied to the bloc's mechanisms indefinitely, which would become an obstacle to the country's independent trade deals elsewhere once it leaves the EU.
Mrs Foster, whose 10 MPs play a critical role in propping up Theresa May's administration in Westminster, said she wants to see a deal struck "that works for everyone", while respecting the result of the referendum.
Britain is keen to move forward on a future relationship, especially after Prime Minister Theresa May's proposals, already in doubt among many of her governing Conservatives, were widely criticised at an European Union summit in Austria last month.
Mrs May told her Cabinet that Britain will not accept an European Union withdrawal deal without a "precise" political declaration setting out how its requirements on trade and security will be delivered.