A draft document from the EU Parliament has suggested Northern Ireland may have to stay in some form of internal market or customs union to prevent a hard border on the island of Ireland.
The draft resolution is set to be voted on ahead of a speech by British Prime Minister Theresa May.
Fourth: Ireland/border: only way there will be no physical infrastructure at border is if UK stays in SM/CU or NI stays in some form of same pic.twitter.com/cShah0DWEL
— Faisal Islam (@faisalislam) September 28, 2017
It comes as the European Union's chief Brexit negotiator has warned it could be "several months" before talks move on to discussions about trade.
Michel Barnier hailed a "new dynamic" to negotiations following Mrs May's speech in Florence last week.
But, speaking in Brussels following the latest round of Brexit negotiations, the European Commission official told UK Brexit Secretary David Davis there is yet to be "sufficient progress" on key withdrawal issues.
"We will need several weeks, even several months, to be able to see 'sufficient progress' on the principles of this orderly departure," Mr Barnier said.
The remaining 27 EU member states have demanded "sufficient progress" be reached on three issues - Britain's possible exit payment, the Northern Ireland border and EU citizens' rights - before negotiations can turn to discussions on a future UK-EU trading relationship.
Mrs May had hoped to breach an impasse on Brexit with her Florence speech, in which she made a commitment on filling an EU budget blackhole and offered new guarantees for EU nationals in the UK.
However, despite praising a "constructive week" for Brexit talks as well as the Prime Minister's intervention, Mr Barnier signalled he will not yet be recommending EU leaders advance negotiations to their next phase.
He said: "We managed to create clarity on some points. On others, however, more work remains to be done and we are not there yet."
At their joint press conference, an "optimistic" Mr Davis claimed "considerable progress" had been made "on the issues that matter".
But he echoed Mr Barnier in conceding there "remain some points where further discussion and pragmatism will be required to reach agreement".
"It is true that there are differences of opinion," he added.
"But with the continued diligence and creativity of our teams, I am confident we can resolve these."
A major sticking point remains over the future role of the European Court of Justice (ECJ), which Mr Barnier suggested should be "indispensable" in ensuring the "consistency" of rights of EU citizens living in the UK.
But Mr Davis warned: "The UK has been clear that, as a third country outside of the EU, it would not be right for this role to be performed by the European Court of Justice."
In her Florence speech, Mrs May told EU member states they will not have to pay more during the bloc's current budget period as a result of the UK's withdrawal, opening up the possibility of Britain handing over €20bn after Brexit.
Calling for more clarity on what Britain was committing to, Mr Barnier said: "For the EU, the only way to reach sufficient progress is that all commitments undertaken by the 28 are honoured by the 28."
The next round of Brexit negotiations will begin on October 9th.
If Mr Barnier agrees "sufficient progress" has been made between the two sides then, he could recommend EU leaders agree move talks on to their next phase when they meet for a European Council summit on October 19th.