Downing Street claims that only a "small number of outstanding issues remain" and that a deal could soon be within reach.
And No 10 sources have confirmed that the "cut off date" for a deal that would pave the way for a November summit of EU leaders is tomorrow mid-morning NZT.
Another UK government source told Reuters that London is closer to securing a deal than it was yesterday.
This means May's emergency meeting would have to be held tomorrow at the latest, allowing time for the EU to summon leaders and organise the summit.
Earlier today, former Foreign Secretary Boris Johnson warned that "no one is fooled" by May's Brexit plans, which he said would amount to the UK's "surrender" and turn the country into an EU colony.
He dismissed the negotiations so far as "theatre," adding that the UK had seen "delay after staged managed delay."
"A deal will be reached and it will mean surrender by the UK. We will be doomed to remain in the customs union and under Brussels' regulatory control. People did not vote for colony status," he said.
He then called on the Cabinet to instead push for an enhanced free trade deal with the EU, based on its relationship with Canada, that is known is Eurosceptic circles as "SuperCanada."
Critics of SuperCanada point out that it would include few provisions for the UK's services industry, which accounts for roughly 80 per cent of the British economy.
It came as May's deputy claimed that a Brexit deal was "almost within touching distance" and suggested an agreement could come within the next 48 hours
David Lidington, the Cabinet Office minister, said the chances of a deal being struck by Friday were "possible but not at all definite".
"We're not quite there yet," Lidington told the BBC's Today programme. "We are almost within touching distance now. The PM has said it can't be a deal at any price."
Asked if he was saying it was possible there could be a deal in the next 24 or 48 hours, he said: "Still, possible but not at all definite, I think pretty much sums it up. Cautiously optimistic."
He stressed that any Brexit deal had to grant the UK a fully independent trade policy.
He also warned that the Irish backstop clause, which is largely to blame for the talks being in deadlock, had to be a temporary measure and that he hopes it was never activated.
