Brexit legislation will return to the House of Lords on Monday with reports suggesting peers will seek to give Parliament a final say on any deal struck with Brussels.
It is reported that a cross-party proposal which would block a "no deal" outcome from the negotiations with the EU will receive backing from the Lords and not be overturned in the Commons.
It had been thought that Britain could simply leave the bloc without an agreement on a future relationship were one not to be struck by March 30 next year, but this amendment would prevent that.
The proposal is aimed at ensuring any agreement forged between the government and EU would be subject to a parliamentary vote and, if rejected, could force the government to recommence talks.
Sir Keir Starmer, the shadow Brexit minister, told the Observer: "This is one of the most important amendments of the entire Brexit process - and indeed of the parliament.
"We have always been clear that the vote must be truly meaningful. It cannot simply be a take-it-or-leave-it choice as the prime minister has suggested.
"This amendment, which has cross-party support, would provide a safety net in the Brexit process. It would remove the possibility of a No vote leading to a 'no deal'. It would bring back control to Parliament."
Prominent Conservative backbencher Jacob Rees-Mogg, who chairs the European Research Group of Tory Eurosceptics, said: "The Lords is putting itself in a very difficult constitutional position. It's decided to take up the banner of 'peers against the people'.
"It is doing its best with a series of amendments - and the one today is particularly important - to stop the referendum result coming into law."
Meanwhile, Democratic Unionist Party leader Arlene Foster has accused the EU's chief Brexit negotiator Michel Barnier of not understanding the "wider unionist culture" of Northern Ireland.
Speaking ahead of Mr Barnier visiting both sides of the Irish border, Ms Foster said: "Michel Barnier's trying to present himself as someone who cares deeply about Northern Ireland and if that is the case he needs to hear the fact that we are part of the United Kingdom (and) will remain part of the United Kingdom constitutionally, politically and economically.
"Therefore his proposal of us being in an all-Ireland regulatory scenario with a border down the Irish Sea simply does not work.
"I don't think he does understand the wider unionist culture of Northern Ireland."