The chief Brexit negotiator has flown to London to resume face-to-face talks with UK counterpart David Frost over the terms of a free trade agreement when Britain begins life outside EU on January 1, 2021. But serious differences still remain, with both sets of negotiating teams refusing to give significant ground on a number of issues, predominantly around fisheries and state aid. French President Emmanual Macron has also been vocal about the EU still having the same access to UK waters over concerns for the future of the French fishing industry.
This had led to fears time will run out to agree a deal that would need to be ratified by both the UK and EU Parliaments before the transition period deadline on December 31.
The European Commission has starting putting pressure on Mr Barnier to agree a trade deal with Britain - according to a report in the Times - raising hopes in Downing Street an agreement could be struck by Friday.
But BBC Europe Editor Katya Adler has tweeted EU diplomats told her they are "nervous" Mr Barnier might be tempted to agree a deal with the UK - "for the sake of his legacy" - but one that would enrage national Governments throughout the bloc.
They fear a deal would offer the UK "too much of a competitive advantage over EU businesses in their own single market" and although Mr Barnier receives widespread EU support, there are now fears they will be "bounced" into a deal as time runs out to agree one.
Brexit news: EU diplomats are nervous Michel Barnier may be 'tempted' to agree a deal with the UK
Brexit news: Michel Barnier is in London to resume trade talks with UK negotiators
EU diplomats have told me they're nervous Barnier might be tempted - for the sake of his legacy - to agree a deal with the UK that national governments eg France/NL object to
Ms Adler tweeted: "Sense amongst a number of member states is quite the opposite to what's been suggested in the article.
"EU diplomats have told me they're nervous Barnier might be tempted - for the sake of his legacy - to agree a deal with the UK that national governments eg France/NL object to.
"Because find too 'lenient', offering UK too much of a competitive advantage over EU businesses in their own single market.
"Broadly Barnier still enjoys widespread EU support but there's nervousness amongst some countries that bc of time running out they'll be 'bounced' into a deal.
READ MORE: EU ordered to rethink fishing plan as UK will ‘NEVER’ accept demands
Brexit news: The BBC's Katya Adler provided insight into the feeling among EU diplomats
“They wouldn't otherwise have accepted. Like UK, EU countries don't want a deal 'at any price'."
She added: “Totally agree with eg @peterfoster the fish focus in UK is red herring.
"For EU the MAIN preoccupation is 'fair competition' ie level playing field. Let's see what this week brings."
European Commission President Ursula von der Leyen has been "quite helpful" and is "keen to unblock things", The Times report added.
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Brexit news: Michel Barnier has resumed face-to-face talks over a trade deal
Brexit news: Ursula von der Leyen has previously warned time is running out to agree a trade deal
She has sent Stephanie Riso, one of her most senior officials, to assist Mr Barnier in talks.
France's foreign minister Jean-Yves Le Drian previously accused the UK of "dragging its feet" in the last-ditch Brexit negotiations.
He added Paris would not back down on the fisheries issues.
On Sunday, Foreign Secretary Dominic Raab said the UK and EU are heading into a "very significant week" as talks over a trade deal enter their final days with several differences yet to be resolved.
Brexit news: The UK is edging towards finally leaving the EU
Several self-imposed deadlines have so far been missed, with negotiations failing to close the gap around differences on competition policy and the distribution of fishing rights.
Mr Raab told the BBC: "This is a very significant week, the last real major week, subject to any further postponement, we're down to really two basic issues.
The Foreign Secretary told Times Radio in a separate interview: "The bottom line is, in the ordinary course of things, we need to get a deal done over the next week or maybe another couple of days beyond that."
When also speaking to Sky's Sophy Ridge On Sunday, Mr Raab said fishing rights remain an "outstanding major bone of contention" with the EU but there is a deal that can still be agreed.
He said: "I do think we're in a reasonable position - there's a deal to be done.
"If you look really at what the outstanding issues are, of course the level playing field, but it feels like there is progress towards greater respect for what the UK position was.
"On fishing there's a point of principle: as we leave the EU we're going to be an independent... coastal state and we've got to be able to control our waters."
Mr Raab said the UK acknowledges the impact on other countries but warned: "I think the answer is 'can the EU accept that point of principle which comes with us leaving the political club?".