But one thing we can't countenance is any idea that there be a three month limit on the backstop.
"The taoiseach [prime minister] indicated an openness to consider proposals for a review, provided that it was clear that the outcome of any such review could not involve a unilateral decision to end the backstop".
Asked about the report, a spokesman at May's office said: "This is all speculation".
The report claims an "all-UK customs deal" will be written into the legally binding withdrawal agreement, which would do away with the need for the controversial "backstop" arrangement agreed by the United Kingdom last December, which would see Northern Ireland remain in full alignment with the EU's single market and customs union rules in the event of a no-deal Brexit.
Hopes of a conclusion for the withdrawal deal being reached this week were dashed after continuous EU-UK talks have ended with "nothing new", according to an EU official.
In a major intervention on the controversial backstop, amid reports that the government plans to keep Northern Ireland in aspects of the European Union trade structures, Mr Davis said it was "pretty clear there is genuine and significant concern regarding the implications of any fresh backstop text".
May is under intense pressure from several members of her cabinet to secure a mechanism by which any backstop agreements can be time limited and able to be terminated by the UK.
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Writing on Twitter, he said: "The Irish position remains consistent and very clear that a "time-limited backstop" or a backstop that could be ended by the United Kingdom unilaterally would never be agreed by Ireland or the EU".
Even if a deal is done in Brussels in the coming days, May will have to sell it in London - first to her own Cabinet, and then to Parliament.
The Brexit secretary is understood to have made his position clear in a meeting with Simon Coveney, the Irish foreign minister, last week. "These ideas are not backstops at all + don't deliver on previous United Kingdom commitments".
He was supported by the EU's deputy chief negotiator Sabine Weyand who tweeted, "still necessary to repeat this, it seems".
Theresa May has apparently worked out a secret deal with Brussels which will keep the United Kingdom in a temporary customs union with the EU.
There appears to be a softening on the EU side to an all-UK customs union replacing the Northern Ireland specific text, but that would require an acceptance by Downing Street that it would in effect be a permanent arrangement. The EU has to date rejected a temporary customs union.
"I think it is possible to get a deal in November", he said.