A “small number of outstanding issues” stand in the way of a Brexit agreement, Downing Street has said after Theresa May updated her cabinet on the talks.
There was “optimism on both sides” after negotiations broke up on Monday night, government sources have said.
But Trade Secretary Liam Fox told the BBC “difficult discussions” were still going on about the Irish border issue.
MPs will vote later on whether the full legal advice about the terms of the UK’s withdrawal should be published.
Ministers are facing possible defeat after an influential group of Tory MPs said they would not oppose Labour’s motion, choosing to abstain instead.
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During a 45-minute discussion on Brexit, the cabinet were briefed on the state of the negotiations, as well as planning for different scenarios ahead of the UK’s scheduled exit on 29 March, 2019.
No 10 said the prime minister had told colleagues progress had been made since the last cabinet meeting a week ago but there were a “small number of outstanding issues as the UK pushes for the best text” and work was continuing.
Ahead of the meeting, Cabinet Office minister David Lidington, who deputises for Mrs May at Prime Minister’s Questions, told BBC Radio 4’s Today “we are almost within touching distance” but warned that “it can’t be a deal at any price”.
Asked to comment on reports that the UK would have to give the go-ahead to major spending on no-deal preparations if there was no agreement by Wednesday, Mr Lidington said “there does come a time at which contingency planning does have to be stepped up”.
The BBC’s Norman Smith said it was thought the only “substantive” area of disagreement left was over the mechanism for the UK to exit the proposed “backstop” customs arrangement – referring to the fallback plans to guarantee there will be no new visible checks on the border between Northern Ireland and the Republic of Ireland.
On Monday night, some cabinet ministers met for drinks in Mr Fox’s office to discuss Brexit, including no-deal plans and the Irish “backstop”.
Mr Fox told the BBC’s Iain Watson there were “still issues” with the backstop and negotiators were having a “number of difficult discussions”.
The prime minister is under pressure from both Brexiteers and pro-EU MPs as she tries to seal a deal with the EU on the terms for the UK’s exit on 29 March 2019.
Another late night
BBC Brussels reporter Adam Fleming
The negotiating teams stayed up late again, but not as late as on Sunday. At issue is the mechanism for terminating the Northern Irish backstop – if it’s ever used.
Should it be a decision for the EU-UK joint committee that will be set up to manage the Brexit treaty or for a separate arbitration panel where UK and EU representatives would be joined by an independent figure from somewhere else?
There is also a tussle within the EU27 over Britain’s idea for a UK-wide customs arrangement as an alternative to the EU’s Northern Ireland-only option.
Some member states see this as giving access to the single market, which should be accompanied by guarantees on other things such as fishing rights and environmental standards.
The European Commission has tried to reassure them, saying it is still only an insurance policy – not the final trade deal – and that it’s just a way to get the British cabinet to approve the Brexit treaty.
Both sides want to schedule a special summit of EU leaders at the end of November to sign off the withdrawal deal, but time is running out.
Brussels says it will only agree to put the wheels in motion for the summit if agreement can be reached on the issue of the Irish border.
If a deal can be reached with the EU in time, Mrs May will then need to persuade her party – and the rest of Parliament – to support it in a key Commons vote.
Boris Johnson, who quit as foreign secretary in July in protest at Theresa May’s strategy, hit out at what he claimed was a “stage-managed delay” in reaching an agreement.
As well as Leave-supporting Conservative MPs who are worried about the UK being tied to EU rules, some pro-EU Tories also have misgivings.
Later on Tuesday, Labour will try in Parliament to force the government to publish, in full, Attorney General Geoffrey Cox’s legal advice on what the backstop and the rest of the withdrawal deal will mean for the UK.
The BBC’s assistant political editor Norman Smith said the government faced potential defeat since the European Research Group of about 40-to-60 Tory MPs was set to abstain on Labour’s motion.
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An alternative proposal by a group of ERG members for a “full reasoned statement” on the legal effect of the withdrawal deal – in effect a summary of Mr Cox’s advice – will not be voted on in the Commons.
In a speech on Monday evening, Mrs May said the “endgame” in the negotiations had been reached and while both sides wanted an agreement, the issues at stake were “immensely difficult”.
On Friday, Transport Minister Jo Johnson became the sixth minister to quit over Brexit, saying what was on offer fell “spectacularly short” of what had been promised and calling for another referendum.
Jesse Norman has been promoted to replace Mr Johnson in the Department for Transport, Downing Street said.
Brexit: ‘Small number of issues’ stand in way of deal}