"We are working towards a deal", said Mina Andreeva, spokeswoman for the European Commission.
"We had a constructive meeting with Steve Barclay and the British team", Mr Barnier told reporters.
Now Irish media are suggesting that the "pathway to a possible deal" most likely involves concessions from Mr Johnson with regards to the border, and that the UK/EU border will instead be in the Irish Sea, between Ireland and the UK, instead of on the island between Northern Ireland and the Republic.
After his meeting with Barclay, Barnier said it was essential to keep focus.
"Be patient", Mr Barnier told reporters as he left the meeting and went on to brief the 27 European Union states. "We need vigilance, determination and patience", said the man who once organized the 1992 Winter Olympics in his Savoie region of France.
French President Emmanuel Macron hinted yesterday that the "next few hours" could be crucial regarding the possibility of a breakthrough on a Brexit deal.
EU Council President Donald Tusk said on Friday morning that "the United Kingdom has still not come forward with a workable, realistic proposal" but tempered that by saying that "even the slight chance (that a deal can be struck) must be used".
"Of course there is no guarantee of success and time is practically up, but even the slightest chance must be used", he added.
The EU's chief negotiator, Michel Barnier, approved an intensification of the discussions after British Prime Minister Boris Johnson and his Irish counterpart, Leo Varadkar, said they could see a "pathway" forward following talks on Thursday.
Sterling see-sawed on the various pronouncements, which came at the end of a tumultuous week in which Brexit negotiations have shifted wildly, starting with a public row between London and Brussels.
Tusk said "there is no guarantee of success and the time is practically up" but insisted both sides should use every opportunity available ahead of Britain's scheduled October 31 departure date.
Barnier was to brief European Union ambassadors and key legislators later Friday, amid a sense that there remains a glimmer of hope to get an amicable divorce deal with Britain.
In Paris, France's European affairs minister, Amelie de Montchalin, had another take on the debate, saying that a no-deal Brexit "is probable, at this stage". If it is time for the sake of time?
"The EU's position remains the same: there must be a legally operative solution in the Withdrawal Agreement that avoids a hard border on the island of Ireland, protects the all-island economy and the Good Friday (Belfast) Agreement in all its dimensions, and safeguards the integrity of the Single Market". "If there is a will, there is a way" she said.