Both Brussels and London have blamed each other for the lack of progress and warned they're running out of patience.
Demands from London over the Northern Irish Protocol risks a "further breakdown in relations" with the European Union, Ireland's Foreign Minister warned on Sunday.
Simon Coveney wrote on Twitter that the UK's demand for the European Court of Justice (CJEU) to be stripped of its oversight of the Protocol would represent a new "barrier to progress that they know EU can't move on."
"Does the UK government want an agreed way forward or a further breakdown in relations," he added.
The UK's Brexit Minister, Lord David Frost, also took to Twitter, writing that "the issue governance and the CJEU is not new."
"We set out our concerns three months ago in our July 21 Command Paper. The problem is that too few people seem to have listened," he added.
Brussels is expected to set out new proposals to break the deadlock over the trade arrangements for Northern Ireland this week.
Frost said the UK "will look at them seriously and positively whatever they say. We will discuss them seriously and intensively."
"But there needs to be significant change to the current situation if there is to be a positive outcome," he also said.
London has been calling for a complete overhaul of the agreement which currently sees Northern Ireland remain in the EU's Single Market with checks to be carried out on certain goods travelling between Northern Ireland and the rest of the United Kingdom.
This effectively creates a de-facto border between Great Britain and Northern Ireland.
The Protocol, negotiated alongside the Brexit Withdrawal Agreement, was seen as the best way to preserve peace by avoiding the creation of a physical border between Northern Ireland and its southern neighbour, the Republic of Ireland, and EU member state. It was backed by parliamentarians in London and Brussels.
Brussels, meanwhile, has said it is open to changes, as long as they are within the framework of the Protocol and suspended its litigation process against the UK over its decision to unilaterally implement grace periods on checks as a sign of goodwill.
Both sides have put the blames on the lack of progress on each other, accusing the other of being inflexible and warning they're running out of patience.
In remarks released ahead of a speech in Lisbon on Saturday, Frost argued that "the role of the European Court of Justice in Northern Ireland and the consequent inability of the U.K. Government to implement the very sensitive arrangements in the protocol in a reasonable way has created a deep imbalance in the way the protocol operates.
Euronews reported on Friday that Brussels is likely to offer unhindered access for products linked to British “national identity,’’ such as Cumberland sausages. The proposal is an attempt to avoid a so-called sausage war over chilled meats crossing the Irish Sea.
Frost’s office on Saturday suggested EU concessions would have to “go far beyond the sausages.”
The British negotiator reiterated last week at the Conservative Party conference that London could trigger Article 16 which allows either side to unilaterally walk away from the deal if a solution is not found soon.
European Commission Vice-President and co-chair of the EU-UK Joint Committee & Partnership Council Maros Sefcovic, told reporters last month that the bloc aims to resolve any outstanding issue before the end of the year.