Cross-party talks between the British government and the Labour Party are expected this week as Theresa May warned that Brexit could "slip through our fingers" unless a compromise can be found.
Shadow business minister Rebecca Long-Bailey, a member of Labour's negotiating team, said it was "disappointing" that there had not been any shift in the government's red lines but "the overall mood is quite a positive and hopeful one".
Labour's key demand is for a customs union with Brussels in order to protect the flow of goods, but Brexiteers vehemently oppose anything that would restrict the UK's ability to strike free trade deals through being bound by tariffs set by the EU.
Ms Long-Bailey told the BBC's Andrew Marr Show that Labour had discussed how any changes to the Brexit agreement "could be entrenched" so that any potential future Conservative leader, such as Boris Johnson, would not be able to "rip up" any compromise - a so-called "Boris-proof" deal.
She said a customs union was "defined in international law" and "the proposals we have seen from the government so far and their direction of travel over the last two years have not been compliant with the definition of a customs union".
But House of Commons Leader Andrea Leadsom said the Prime Minister's deal with Brussels already had a "customs arrangement" in it aimed at tariff-free trade.
She added: "My expectation - and I'm not party to the discussions - is that the Prime Minister will only seek to agree those things that still constitute Brexit."
The Prime Minister heads to Brussels on Wednesday for an emergency summit aimed at securing a further delay to Brexit, with Mrs May hoping for an extension until 30 June at the latest, with the option of leaving the EU earlier if a deal can get through Parliament.
If no extension is agreed then the UK is set to leave without a deal on Friday.
Ms Long-Bailey suggested Labour could be prepared to revoke Article 50, cancelling Brexit, if the UK was heading towards a no-deal scenario.
"We have promised our party members and our constituents that we will do all we can to avoid a no-deal situation and it's something that we would consider very, very strongly," she said.
Signalling that talks aimed at reaching a deal with the Tories were expected to continue she said "hopefully at the beginning of next week we will be having further discussions".
"But we are currently waiting for the government to come back to us now to state whether they are prepared to move on any of their red lines," she said.
Ms Long-Bailey also said that Labour had raised the prospect of a second referendum to prevent a "damaging" or no-deal Brexit.
Some 80 MPs, including frontbenchers, have written to Jeremy Corbyn demanding a public vote on any deal that emerges from the talks.
Brexiteer Mrs Leadsom said she would never back the revocation of Article 50, insisting the UK could "survive and thrive" after a no-deal exit and it would be "not nearly as grim as many would advocate".
The Commons Leader said the Tories were working with Labour "through gritted teeth", adding that a second referendum is an "appalling" idea and taking part in the European elections would be "utterly unacceptable".
The Prime Minister said she had done "everything in my power" to persuade Tory and DUP MPs to back her deal, but acknowledged the Withdrawal Agreement had been rejected by the Commons three times and "there is no sign it can be passed in the near future".
"Because Parliament has made clear it will stop the UK leaving without a deal, we now have a stark choice: leave the European Union with a deal or do not leave at all," she said in a statement.
Defending the cross-party approach, she said: "The fact is that on Brexit there are areas where the two main parties agree: we both want to end free movement, we both want to leave with a good deal, and we both want to protect jobs.
"That is the basis for a compromise that can win a majority in Parliament and winning that majority is the only way to deliver Brexit."
But she warned that "the longer this takes, the greater the risk of the UK never leaving at all".
"It would mean letting the Brexit the British people voted for slip through our fingers. I will not stand for that."
Tory Eurosceptics are furious at the Prime Minister's handling of the Brexit process.
European Research Group chairman Jacob Rees-Mogg told Sky News: "The Prime Minister could have taken us out on 29 March. It was the Prime Minister who asked for an extension, it was the Prime Minister who changed the date by prerogative power from 29 March to April 12.
"This all rests with her and upon her shoulders. The Prime Minister, Mrs May, has made active choices to stop us leaving and she deserves to be held to account for that."
Ex-whip Michael Fabricant predicted "open revolt" in the Conservative Party and among Leave voters if Mrs May agreed to a customs union.
The Sunday Telegraph reported that Conservative activists are refusing to campaign for the party and donations have "dried up" because of Mrs May's leadership.
In a letter to the Prime Minister, more than 100 current and would-be Tory councillors state that they are unable to muster the volunteers needed to effectively fight next month's local elections because "belief in the party they joined is gone".
Former Brexit secretary Dominic Raab said Mrs May's approach "threatens to damage the Conservatives for years" and that teaming up with Mr Corbyn could be "potentially disastrous for the nation".
Writing in the Mail on Sunday, he said: "There is now a danger that Brexit could be lost and that the government could fall - handing the keys to Downing Street to Corbyn."