Brexit Secretary Stephen Barclay is in Brussels for talks, amid growing EU pessimism over whether a new withdrawal deal can be agreed.
The EU’s chief negotiator, Michel Barnier, told diplomats the UK’s proposed alternative to the Irish backstop was unworkable.
And BBC Brussels reporter Adam Fleming described the mood as “downbeat”.
Downing Street said “progress has been made” but there were still “significant obstacles” to reaching a deal.
Our correspondent said European diplomats thought the chances of finalising a new Brexit deal by a crucial EU summit on 17 October were “dwindling”.
The UK is scheduled to leave the EU on 31 October, although MPs have passed a law requiring Prime Minister Boris Johnson to seek an extension to that deadline from the bloc if he is unable to pass a deal in Parliament, or get MPs to approve a no-deal Brexit, by 19 October.
Mr Barclay and Mr Barnier will discuss alternatives to the Irish backstop, which aims to avoid a hard border on the island of Ireland after Brexit.
The policy is unacceptable to many Conservative MPs, and Mr Johnson has insisted a revised Brexit deal must include “the abolition of the backstop”.
The EU’s chief Brexit negotiator, Michel Barnier, has given a downbeat assessment of talks with the UK to EU ambassadors in Brussels.
During a briefing ahead of Mr Barclay’s visit, he said the UK was picking and choosing from EU laws, and that none of the ideas were fully worked out.
Separately, European diplomats believe the chances of finalising a revised Brexit agreement by the next summit of EU leaders on 17 October are dwindling.
They think Wednesday’s fractious scenes in the House of Commons suggest the prime minister has alienated Labour MPs who might have supported a deal.
Some EU officials are preparing for the political turbulence in the UK to continue for several years.
It’s a pessimistic backdrop for the Brexit secretary’s visit later.
But ahead of Friday’s meeting, Mr Barnier said the UK government’s proposed solution to the backstop would put the single market at risk.
He said the UK’s ideas so far involved managing different rules for customs and products on either side of the Irish border, rather than keeping them the same across the whole island.
The chief negotiator also claimed the UK’s concept of a plant and animal health zone would require the EU to unravel some of its own rules.
The UK prime minister’s spokesman acknowledged there was a “long way to go” before a deal could be reached.
The European Parliament’s Brexit co-ordinator, Guy Verhofstadt, who met Mr Barnier on Thursday, said the UK’s proposals to resolve the Irish backstop issues “fall short”.
He insisted any plan must work to “preserve consumer safety, to protect our businesses and preserve the peace”.