Discussions between the two officials and their teams concluded a day early last week, with Mr Barnier claiming there were “serious divergences”.
The EU official last week added that he was looking forward to the next round of talks due on July 20 – but there was no mention of extra talks now pencilled in for today and tomorrow.
Mr Barnier has said that the UK has set out a number of requests on their side of the deal, and has claimed that the EU has “engaged constructively” with these.
He then stated that the EU expects its own position to be “better understood and respected” in turn if a deal is to be reached.
Mr Frost, meanwhile, said of last week’s talks that the meetings had been “comprehensive and useful” but that there were “significant differences” on a number of issues.
So far, these are understood to involve competition rules and systems for settling disputes, among other things.
The UK and EU have been engaged in post-Brexit trade talks for months, though progress has been slow and limited.
It’s understood that today’s talks will extend on to Wednesday – though it’s unclear whether or not these constitute a ‘round’ of negotiations or something more informal.
The next official round is due on the week beginning July 20.
Last month, UK Prime Minister Boris Johnson and EU presidents Ursula von der Leyen, David Sassoli and Charles Michel agreed that the negotiations needed a “new momentum”.
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The pressure is on for the UK and the EU to agree to terms of their future trade relationship post-Brexit, especially since Boris Johnson confirmed that the UK would not seek an extension to the current transition period.
This period runs to the end of this year. If, by January 1 2021, there is no agreement in place, then the UK will have gone through a ‘no-deal Brexit’.
Opponents of a no-deal Brexit fear the economic impact it would have on businesses and institutions given the overnight change in trading rules that would apply.
Mr Johnson, however, appears confident that such a situation won’t arise.
He claimed in mid-June that he saw no reason why a Brexit deal could not be in place by the end of this month.
Mr Barnier, despite his concerns that little progress had been made, said last week that he still believed a Brexit agreement was possible and that it would also be “in everyone’s interest”.
He said: “We look forward to the next round of negotiations in the week of 20 July.”