Theresa May is to chair a special cabinet meeting on Wednesday to discuss a draft Brexit withdrawal agreement.
A cabinet source has told BBC the text has been agreed at a technical level by officials from both sides after intensive talks this week.
The Sun reported that every minister was being asked to see the PM for one-to-one talks on Tuesday evening.
The future of the Irish border has been the last major outstanding issue to be settled in the negotiations.
Earlier, ministers said they would publish a “full legal statement” before MPs vote on any final agreement.
The undertaking was given as the government faced near certain defeat in the Commons over whether to publish the legal advice it gets about the terms of the UK’s withdrawal.
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Cabinet ministers were briefed on the state of the negotiations earlier on Tuesday, at which they were told a “small number of outstanding issues” remained to be sorted.
BBC chief political correspondent Vicki Young said individual cabinet ministers were likely to be shown the full draft text this evening as a prelude to a full meeting on Wednesday afternoon.
She said they would have to decide whether they could support it, and if not, whether to resign from cabinet.
In another development, ambassadors from the remaining 27 EU states will meet in Brussels on Wednesday.
The prime minister has been 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 the UK and EU want to schedule a special summit of European 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.
Following pressure from all sides of the House of Commons, ministers have agreed to provide MPs with a legal assessment of the implications for the UK of the backstop and other controversial aspects of any deal.
The Democratic Unionists, on whom the PM relies for her Commons majority, said they would vote for Labour’s motion urging disclosure of “the full and final advice” given by Attorney General Geoffrey Cox to the cabinet.
An influential group of Tory Brexiteers also said they would not oppose the move, which was later passed unopposed in the Commons.
Cabinet Office minister David Lidington said Mr Cox, who is the government’s senior legal adviser, would make a statement to MPs and take questions ahead of the final vote on any Brexit deal.
MPs, he said, would get to see “a full reasoned position statement laying out the government’s both political and also legal position on the proposed withdrawal agreement”.
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The concession reflects the wording of a compromise amendment supported by a number of Tory members of the European Research Group which was not selected for debate.
The DUP’s Westminster leader Nigel Dodds said he was pleased Parliament had “asserted its will” as it was imperative that all parties to the deal were clear in what way and for how long it would “legally bind” the UK.
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”.
But 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.
Brexit: Theresa May calls special cabinet meeting as draft deal agreed}