The meeting between the two men came a day after British Prime Minister Boris Johnson and his Irish counterpart Leo Varadkar had a "detailed and constructive discussion" in which they agreed that a Brexit deal is possible.
It should become clear by tomorrow whether an agreement is possible - and it would be finalised at a crucial summit in Brussels on Thursday and Friday.
Barnier emerged from a two-and-a-half hour long meeting with the UK's Brexit Secretary Steve Barclay in Brussels on Friday, telling reporters that they need to be patient as "Brexit is like climbing a mountain".
Johnson has to work on two fronts after he has drafted a plausible deal: get it passed in the British Parliament by October 19 as per the Benn Act and get the European Union to sign it before October 31.
But the House of Commons leader said the PM could be "trusted" to deliver, and that the mood was "more positive" than it had been a week ago.
"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".
This "binary choice", as one government source called it, will pose a dilemma for Brexiteers in particular, as the PM's softened stance on some aspects of the Brexit deal appear to cross red lines set out by Mr Johnson himself. However, Johnson and Varadkar "both saw for the first time a pathway to a deal... even the slightest chance must be used".
Iran women freely attend football match for first time in decades
During last year's World Cup, female fans were allowed to watch a broadcast at the same stadium of Iran's game against Spain. Amnesty International called the decision "a cynical publicity stunt by the authorities meant to whitewash their image".
Sir Keir also pledged that Labour would do "whatever it takes" to stop a no-deal Brexit at the end of the month.
"Those who know anything about Northern Ireland will appreciate that these issues will only work with the support of the unionist as well as the nationalist community", she said in a statement.
If speculation is correct, it would create a customs border in the Irish Sea with goods travelling from the rest of the United Kingdom to Northern Ireland being subject to tariffs which Britain would collect on behalf of the EU.
With UK officials remaining tight-lipped, there has been intense speculation over what was said at the talks at Thornton Manor which enabled the process to move forward.
Seeking to ensure that Johnson's minority government is not able to hold a general election on his terms, with the Tories claiming to represent the "will of the people" on Brexit, as defined by the 2016 referendum result, they have stepped up their plotting.
The province would however benefit from lower tariffs agreed with countries as part of any new trade deals.
The EU's chief negotiator Michel Barnier is then due to brief EU ambassadors and MEPs tomorrow on progress in the talks.