But May's room for compromise is limited because her minority government is propped up by the Democratic Unionist Party, a pro-British party that fiercely opposes any separate status for Northern Ireland.
It is understood that cabinet ministers Liam Fox, Michael Gove, Dominic Raab and Jeremy Hunt expressed concerns.
The Guardian said House of Commons leader Andrea Leadsom was also concerned about May's reported plan to accept keeping Britain in the EU customs union for an indefinite period after it withdraws.
European Union Commissioner Guenther Oettinger said Friday that he sees room for a breakthrough in the talks next week, when leaders from the 27 EU nations meet with British Prime Minister Theresa May.
Barnier said on Wednesday that "administrative procedures" would be required on goods travelling to Northern Ireland from the rest of the United Kingdom if the border is to remain free-flowing.
He warned: "She know the consequences if she walks away from that promise, not just for Northern Ireland, because of course she will open a Pandora's box in Scotland as well".
Agreeing on how to maintain an open Irish border after Brexit is the key hurdle now to sealing a divorce deal between the European Union and Britain.
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.
"This is the problem with the policies of both major parties: they seem to think you can do Brexit and then engage is a whole lot of social legislation to make capitalism fairer and more equal and so on", Blair said.
Following three days of talks with key figures in Brussels, DUP leader Arlene Foster said the Prime Minister could not in "good conscience" accept the proposals now on the table from the EU.
The document was one of 29 technical papers released by Government departments on Friday, in the final tranche of guidance on preparations for a no-deal Brexit.
"When we published our plans in June on a UK-wide customs backstop, we were absolutely clear that the arrangement would be temporary, and only in place until our future economic relationship is ready", the spokeswoman said.
Finance minister Philip Hammond said there had been a "measurable change in pace" in talks in the last 10 days, but there were "some big differences left to resolve".
Asked about the threat, May said: "The DUP will do what the DUP will do".
Following the meeting, ahead of next week's crunch summit in Brussels, the government Chief Whip Julian Smith insisted ministers were fully behind Mrs May's negotiating strategy.
He added: "Agreement is within reach if we have the negotiations on October 17 at the next council meeting".
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