He said he hoped that during their single day of talks, he and Mr Davis would be able to identify priorities and a timetable for the ongoing negotiations, so that he can report back to leaders of the other 27 EU states at the European Council summit in Brussels on Thursday.
The working language of the negotiations will be English and French, with interpretations provided by the European Commission.
Britain on Monday began formal talks on its upcoming exit from the European Union, almost a year after the country had voted to to leave the EU in a referendum.
The talks will initially focus on three areas insisted on by the EU - Britain's Brexit bill, estimated at around 100 billion euros (Rs 7,200 billion), the rights of three million EU nationals living in Britain and one million Britons on the continent, and the status of the border between Northern Ireland and Ireland. An early election this month, in which British Prime Minister Theresa May lost her Conservative majority in parliament, only added to the problems.
Frenchman Barnier struck a firm tone as he said the timetable for Britain's divorce after four troubled decades of membership made sense.
He added: "It's not as if Europe is leaving Britain; Britain wants to leave the EU".
Davis said in a statement Sunday: "Now, the hard work begins". "An overly blinkered approach focused on simply cutting immigration to tens of thousands and focusing only on high skilled employees could leave employers high and dry, especially those who rely on European Union migrants to fill low-skilled jobs", Davies said. We keep hearing that they don't want a 'Norway model, ' they don't want a 'Swiss model, ' they want to leave the customs union, the internal market, they want to limit migration.
Anxious by immigration and loss of sovereignty, Britons voted last June to become the first nation ever to leave the 28-nation EU. There is more that unites us than divides us.
And even when May finally triggered the two-year unraveling process on March 29, she followed it up by calling an early election on June 8 that she hoped would strengthen her majority in parliament and thus her negotiating mandate with the EU.
Barnier however said that "a fair deal is possible and is far better than no deal - that is what I said to David today".
Brexit Secretary David Davis has said Britain will seek "a deal that works in the best interests of all citizens" in Brexit talks getting under way in Brussels.
European Union officials had earlier warned May not to make that offer so early in the talks.