The Irish backstop measure, created to ensure no new border emerges between Ireland and Northern Ireland, is supposed to be temporary until a UK-EU trade deal can be agreed, and Theresa May pledged earlier this year that the arrangement would expire "at the very latest by the end of December 2021".
The DUP has predicted "developments" in the government's Brexit position this weekend, after the party threatened to withdraw support for Theresa May if she caves in to Brussel's demands for a border in the Irish Sea.
Mrs Foster previously said that the prime minister could not "in good conscience" recommend a Brexit deal that places a trade barrier on businesses moving goods from one part of the United Kingdom to another.
Tory Brexiteers fear that she is about to concede to European Union demands that it must be open-ended, despite previous assurances from ministers it would have to be time-limited.
The UK and the European Union both want to avoid a "hard border" - physical checks or infrastructure between Northern Ireland and the Republic of Ireland - but can not agree how.
"There should not be international-style borders within it", she wrote in the paper this morning.
They added that to wait until Tuesday's Cabinet meeting and somehow "bounce" ministers into supporting her deal would be "the worst possible way of doing it".
"Indeed, Northern Ireland's access to any new United Kingdom trade deals would also be regulated by Brussels".
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"But it is true that there needs to be a period, probably following the transition period that we have negotiated, before we enter into our long-term partnership, just because of the time it will take to implement the systems required".
Juncker said that the EU Commission and member states were preparing for a potential "no deal" scenario that would see Britain crash out of the EU next March without legal agreements governing its relations with the rest of the bloc.
In a shot across Mrs May's bows, Dominic Raab, the Brexit Secretary, also made clear his opposition to concessions on the backstop.
There is no hard border at present, as goods and services are traded between the two countries with few restrictions as both are now part of the EU single market and customs union.
Work and Pensions Secretary Esther McVey, who wasn't at the meeting, has repeatedly refused to endorse the prime minister's Chequers blueprint for Brexit.
Eurosceptics want a time limit for how long Britain will keep following the EU's customs rules before it can strike out on its own and sign independent trade agreements with new partners.
In addition, Northern Ireland would remain under large parts of single market regulations, requiring enhanced checks on products arriving from Britain, particularly agricultural goods.