After the Irish prime minister (or "taoiseach") Leo Varadkar suggested that a deal could still be done on-time following one-on-one talks with Prime Minister Johnson and a meeting between Barnier and Britain's Brexit Secretary Stephen Barclay, however, the word has gone out that "tunnel" negotiations may (or may not) be on the cards - although few reporters have elaborated on what this actually means. "Whatever it takes, we will prevent a no-deal Brexit".
Following the briefing, representatives from the 27 member states gave Barnier the green light to "intensify" talks.
The discussions focused heavily on the issues of the customs arrangements and the proposed "consent" mechanism for the Northern Ireland Assembly. "I have already said that the Brexit is like climbing a mountain and we need vigilance, determination and patience".
Tusk, speaking in Nicosia, said "for the first time" Varadkar and British Prime Minister Boris Johnson saw a pathway toward a divorce deal for Britain's departure from the European Union.
Boris Johnson's government is set to enter intensive "tunnel" negotiations with the European Union over a possible Brexit deal ahead of a crunch summit in Brussels next weekend, in a major boost for the prospect of an agreement before the October 31 deadline. But Johnson has insisted that Britain is leaving on October 31 "do or die" - with or without a divorce deal.
Donald Tusk, the European Union council president, said on Friday he had told the prime minister to present his Brexit proposals to the European Union by next Thursday but added that "positive signals" were now emerging from London.
Johnson has insisted that Britain will leave the European Union at the end of the month on the scheduled Brexit date of October 31 regardless of whether there is a deal or not.
With parliament set to sit in a special emergency Saturday session at the end of the week, Mr Starmer said it appeared any agreement Mr Johnson was able to negotiate would be "even worse" than Theresa May's rejected deal.
Johnson said that there was a "pathway" to a belated deal to stave off a chaotic and costly no-deal Brexit on October 31, while Varadkar said the meeting was "very positive".
The UK presented alternative plans last week which would see Northern Ireland remains in the customs union for goods and agri-food products with physical checks to be conducted away from the border.
However, Italian newspaper Repubblica has quoted Nigel Dodds, deputy leader of the DUP, as saying that Mr Johnson's proposed solution to break the Brexit deadlock can not work because Northern Ireland must remain in a full United Kingdom customs union.
On Friday Mr Johnson said there was "a way to go" before a deal could be reached.