Brexit Secretary Dominic Raab has held last-minute talks with EU counterpart Michel Barnier in Brussels - but government sources have told ITV News a deal has not been done.
Mr Raab spoke with Mr Barnier for an hour and a half at the EU commission in Belgium with the Northern Irish backstop among the points of discussion.
All 27 EU ambassadors were summoned to receive a briefing from Mr Barnier in the aftermath of the meeting, raising the prospect of an imminent deal between the negotiators.
The hastily arranged talks came as Mr Raab's predecessor David Davis urged cabinet ministers to "exert their collective authority" over EU exit plans ahead of Wednesday's summit.
Brand earlier said Mr Raab's unscheduled rush to Belgium on Sunday suggested "things (were) moving fast" in negotiations.
Brand said a new "review clause" for the Northern Ireland backstop was among options discussed by Mr Raab and Mr Barnier in Brussels.
Government sources also urged against snap interpretations of the Brexit secretary's rush to the continent.
Brand also understands from sources that Leader of the Commons Andrea Leadsom is "still considering her position" ahead of what looks to be a crunch cabinet meeting on Tuesday.
The Sunday Times said at least nine ministers want Mrs May to change course when the Cabinet meets on Tuesday.
Speculation about possible resignations has centred on Mrs Leadsom, Penny Mordaunt and Esther McVey.
But the newspaper also indicated that Scottish Secretary David Mundell and Scottish Tory leader Ruth Davidson could quit because special arrangements for Northern Ireland could fuel the case for Scottish independence.
Mrs May’s own position also appeared in jeopardy, with as many as 44 letters demanding a vote of no confidence reportedly submitted to the Conservative 1922 Committee – just four short of the number required to trigger a ballot.
Tory MP Nadine Dorries suggested that Mr Davis should be installed as interim leader, claiming that was the only way to secure the kind of free-trade deal Brexit demanded by Eurosceptics.
Ex-minister Mr Davis earlier branded the prime minister's plan "completely unacceptable," as Mrs May is forced to face increasing pressures within her party and from her DUP allies over Brexit as a key summit with EU leaders looms.
As negotiations continue in Brussels ahead of a summit starting on Wednesday, the Prime Minister faces a political battle over a plan which could keep the UK in a customs union to avoid a hard border with Ireland.
Meanwhile Democratic Unionist Party leader Arlene Foster is reported to have said that a no-deal Brexit was now the most likely outcome after talks with senior figures including Michel Barnier in Brussels.
Her party is opposed to any customs arrangement which would result in Northern Ireland being “annexed” or impose extra checks on goods travelling to or from Great Britain.
With continued speculation that Leave-supporting Cabinet ministers could resign if Mrs May presses ahead with the plan, David Davis said: “This is one of the most fundamental decisions that government has taken in modern times.”
Writing in the Sunday Times he added: “It is time for the Cabinet to exert their collective authority. This week the authority of our constitution is on the line.”
The issue of the border between Northern Ireland and Ireland is one of the last remaining obstacles to achieving a divorce deal with Brussels, with wrangling continuing over the nature of a “backstop” to keep the frontier open if a wider UK-EU trade arrangement cannot resolve it.
The European Union’s version, which would see just Northern Ireland remain aligned with Brussels’ rules, has been called unacceptable by Mrs May and is loathed by the DUP.
Mrs May’s counter-proposal is for a “temporary customs arrangement” for the whole UK, but Tory Brexiteers are suspicious this could turn into a permanent situation, restricting the freedom to strike trade deals around the world.
The Northern Irish situation is politically problematic for Mrs May because her minority administration depends on the votes of the 10 DUP MPs.
A leaked email reported in the Observer indicated Mrs Foster was ready to block a Brexit deal.
According to a private email exchange between senior UK officials, seen by the newspaper, Mrs Foster gave her views during a dinner with the leader of Conservative MEPs, Ashley Fox.
The leaked email said Mrs Foster described the EU’s chief Brexit negotiator Mr Barnier as “difficult and hostile” and indicated “the DUP were ready for a no-deal scenario, which she now believed was the likeliest one”.
Writing in the Belfast Telegraph on Saturday, Mrs Foster said she appreciated the risks of a no-deal Brexit but “the dangers of a bad deal are worse”.
She added: “The DUP’s actions this week are not as some have suggested about ‘flexing muscle’.
“This is no game.
“Anyone engaging in this in a light-hearted way foolishly fails to grasp the gravity of the decisions we will make in the coming weeks.”
A further demonstration of Tory resistance to Mrs May’s plans came from MP Anne-Marie Trevelyan, who wrote in the Sunday Telegraph that “the idea of remaining in the customs union – even it if is called a ‘temporary customs arrangement’ – after the end of the transition period, in to the 2020s, means simply delaying Brexit and causing the 17.4 million people who voted for it to lose faith in our democracy”.
Jacob Rees-Mogg, chairman of the European Research Group of pro-Brexit MPs, warned that when it came to the backstop proposal “temporary means eternal”.