"In short term, ministers told be ready for another Cabinet meeting, maybe even at end of this week, because there might be enough movement by then to push button on a deal", she tweeted after the meeting.
It comes as the Irish Prime Minister reminds the United Kingdom it's signed up to a legally operative backstop to avoid a hard border.
"While the United Kingdom should aim to conclude the Withdrawal Agreement as soon as possible, this would not be done at any cost".
Crucially, the speculated new deal will contain an "exit clause" that May hopes will show Eurosceptiocs that the United Kingdom will not remain in a customs union with the EU indefinitely.
Following the Cabinet meeting, Mrs May's spokesman said: "The Prime Minister said she was confident of reaching a deal".
Officials at the attorney general's office and the Brexit department are now drawing up plans for a system by which the United Kingdom could end a temporary customs arrangement with the European Union without Northern Ireland being treated separately.
Irish Foreign Minister Simon Coveney has insisted that a time-limited Brexit backstop will never be agreed by the Irish Government or the EU.
Tory Brexiteers fear the United Kingdom could be left permanently under a backstop agreement with Brussels, curtailing Britain's ability to sign independent trade deals, with Mrs May having told the European Union this cannot be the case.More news: Manchester City could face UEFA sanctions over alleged financial doping
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A spokesman for Mr Varadkar said: "The Taoiseach 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".
Varadkar separately told reporters that an expiry date of that nature would not be worth the paper it is written on.
Work is continuing on this, he said, adding: "Don't be under any illusions that there remains a significant amount of work to do".
At a news conference in Slovakia, the EU's chief Brexit negotiator Michel Barnier reiterated Brussels' support for Ireland's position on a backstop arrangement, as he repeated an overall Brexit deal has yet to be reached.
Meanwhile she was said to be on course to approve an economic partnership with the European Union which could develop into a Canada-style free trade arrangement. "And a backstop can not have a time-limit".
Prime Minister Theresa May called a meeting Tuesday in what pundits say was a last ditch attempt at persuading colleagues to back a plan that could ultimately see all of the United Kingdom remaining inside the EU customs union, with all that would entail, in the event a Brexit-trade deal cannot eventually be reached.
Mr Matheson, speaking in Treasury questions, said: 'The Government's own figures demonstrate between a 2% and 8% hit on the broader economy on Brexit, so isn't it the case that there is no form of Brexit that won't have a massive impact on the public finances and therefore on public services?'
"Looks like we're heading for no deal", he tweeted.