The clock is ticking down ahead of Britain's planned departure from the European Union on October 31. The deal being negotiated would smooth Brexit by ensuring that EU rules continue to apply in Britain during a transitional phase.
Experts on both sides have reached agreement on some of the thorniest issues, Barnier told EU ambassadors according to diplomats.
This includes customs controls for goods passing between Northern Ireland - a part of the United Kingdom - and EU member Ireland, a consent mechanism for Belfast and pledges to meet EU standards in areas such as social and environmental provisions.
But the two sides were still locking horns late Wednesday over the issue of value-added tax regimes. At stake is how to collect VAT on goods passing between Britain and the EU and the need to protect the bloc against VAT fraud.
German Chancellor Angela Merkel and French President Emmanuel Macron were cautiously optimistic Wednesday of reaching a deal. "The news out of Brussels could be worse," Merkel said after joint government talks.
European Council President Donald Tusk said talks were going in the "right direction," while referring to a "complicated" situation in the British parliament, whose backing will be needed.
"Yesterday evening I was ready to make a bet that the deal is ready and accepted. Today again some doubts appeared from the British side," he told the Polish broadcasters TVN24 and Polsat News.
The key sticking points have been provisions to avoid a hard border between EU member Ireland and Northern Ireland, which will leave with the rest of the United Kingdom. The open border is crucial to a Northern Irish peace deal signed over 20 years ago.
British media reported earlier that London had made fresh customs concessions, effectively paving the way for a customs border down the Irish Sea between mainland Britain and Northern Ireland.
A similar scenario had been ruled out by former British prime minister Theresa May in an earlier stage of negotiations.
Johnson rejected the Irish border provisions that May eventually agreed with Brussels. He has long hoped to secure a revised deal at this week's EU summit.
Brussels is adamant that negotiations will not take place at the summit, meaning that a breakthrough would have to be achieved beforehand, or else talks would likely continue afterwards.
Speculation has also been rife on a possible further Brexit delay, an option that Johnson has sought to reject.
Irish Prime Minister Leo Varadkar, who spoke to Johnson by phone early Wednesday, said he was "convinced that all parties are serious about getting an agreement by the end of this month."
Any deal agreed by EU leaders will then have to be approved by British and EU lawmakers.
Johnson has no majority in parliament, which is deeply divided over Brexit, leaving the outcome of any votes uncertain. One key player is Northern Ireland's Democratic Unionist Party (DUP), which has close links to the ruling Conservatives.
Johnson met DUP leader Arlene Foster for one-and-a-half-hour talks on Tuesday. The party has concerns about the proposed customs border.
"Discussions continue," Foster later tweeted, indicating that differences remain.
In London meanwhile, Brexit Secretary Stephen Barclay told lawmakers that Johnson will comply with a new opposition-led law that requires him to ask the EU for a three-month Brexit delay, unless parliament approves a deal or votes in favour of a no-deal Brexit by Saturday.
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