The Irish border has proved the biggest obstacle to a deal, with both sides vowing not to reinstate a hard border between Ireland and Northern Ireland for fear of destabilizing a peace accord that ended decades of deadly sectarian violence.
The Sunday Times claims the Prime Minister is optimistic that her secret plan will convince some remainer Conservatives and swithering Labour MPs to back the deal.
However, if these Brexiteers are not convinced that the customs union is only a temporary measure they would nearly certainly rebel.
Mr Raab's proposal was put to the Irish deputy prime minister Simon Coveney in a private meeting in London last Tuesday, but three days later was apparently contradicted by David Lidington, the UK's de facto deputy prime minister, on a visit to Dublin.
Downing Street has insisted it does not have a deal ready for signoff, in response to reports over the weekend of there being an agreement in the making.
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Brexit talks have been deadlocked over the so-called backstop - the fallback position that would be activated if a future EU-UK trade deal does not produce a solution that would prevent a hard border between Ireland and Northern Ireland.
According to the Sunday Times, the private concessions will prevent the need for Northern Ireland to be treated differently to the rest of the United Kingdom - and avoid an Irish backstop.
Yet all the signs are that the European Union are not prepared to accept anything that would either put a time-limit on the backstop, or allow the United Kingdom to end it unilaterally.
Theresa May is preparing a Brexit deal to keep the whole of the United Kingdom in a customs union with the EU, according to a report.
At the same time, it reported that the prime minister was on course to agree a future economic partnership that would leave open the possibility of Canada-style free trade deal sought by Brexiteers.
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Following a phone conversation with Mrs May on Monday morning, the Taoiseach said both leaders emphasised their commitment to avoiding a hard border in Ireland and the need for a legally operable backstop.
He added: "We hope a deal can be done but we're not there yet".
"In March the United Kingdom agreed this backstop will apply "unless and until" a close future relationship eliminates any need for border infrastructure or related checks and controls".
Speaking to Sky News on Monday on whether Theresa May can get a Parliamentary majority to pass her Chequers Plan, which would leave the United Kingdom tied to numerous bloc's regulations, Mr Farage said: "In classic Brussels style, at the 11th hour there will be a deal, I've no doubt about that".
"While we too hope the Northern Ireland backstop will never be required to be used, it will be required to be written down in legal text".
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"By voting for May's deal they can say to their constituents "I voted for us to leave the European Union", even if the detail means we haven't really".