Playing down reports that she is close to a deal with the EU, Mrs May will tell ministers that the key sticking-point remains how to avoid a "hard border" between Northern Ireland and the Republic after Brexit.
The agreement would avoid the need for an Irish backstop - which has left Britain and Brussels deadlocked - and would stop Northern Ireland being treated differently to the rest of the UK.
Asked about the government's position on the Irish backstop, the spokesman said: "The position that we have set out is we don't want the backstop to be in place indefinitely and we will be looking to a mechanism to achieve that".
During a phone call between Leo Varadkar and the Prime Minister on Monday, Mr Varadkar said that the outcome of a review could not involve a unilateral decision to end the backstop.
May later reiterated to Austrian Chancellor Sebastian Kurz that she believed a withdrawal accord was 95 per cent complete, and was "confident" of a deal on the Northern Irish backstop.
But Downing Street has reportedly dismissed the report as "speculation".
The conversation followed a Daily Telegraph report that Brexit Secretary Dominic Raab has privately demanded the right to pull Britain out of the Irish backstop after just three months.
"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".
Irish Foreign Minister Simon Coveney has insisted that a time-limited Brexit backstop will never be agreed by the Irish Government or the EU.
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The two sides now have only days left to bridge the remaining gap in order for an European Union summit to be called this month that could sign off a divorce agreement.
Waterstones chief executive James Daunt, ex-Sainsbury's chief executive Justin King, Lastminute.com founder Baroness Lane-Fox and Innocent Drinks co-founder Richard Reed were among signatories of a letter calling for a People's Vote on leaving the European Union.
The EU has proposed a backstop that would mean Northern Ireland staying in the EU customs union, large parts of the single market and the EU VAT system.
Meanwhile, 1400 of the UK's top lawyers have urged Theresa May and MPs to back a second Brexit referendum, saying that "democratic government is not frozen in time".
However, the newspaper also reported that the new deal will include an "exit clause" created to convince those who support Brexit that remaining in the customs union is only temporary.
While the European Union has refused to accept a backstop that does have a time-limit.
They suggested that a December deal would mean not only a later parliamentary vote but would require spending on no-deal planning and changes to the roles of hundreds of civil service.
There will be an "exit clause" from the customs union in a bid to convince Brexiteers that it is not a permanent arrangement as May looks to secure enough votes to get the deal through parliament, said the paper.