There are increasing indications that an agreement on the first phase of Brexit talks is about to be struck.
EU Council president Donald Tusk said he was "encouraged by progress" and a deal on Ireland, the "divorce bill" and citizens' rights was "getting closer".
Theresa May is meeting EU figures in an attempt to finalise the deal ahead of a summit in 10 days' time.
Belgian MEP Philippe Lamberts told the BBC's Laura Kuenssberg that the UK had made a concession on the Irish border.
The BBC's political editor said Mr Lamberts said the UK was prepared to accept that Northern Ireland may remain in the EU's customs union and single market in all but name. But, she stressed, the BBC has not yet seen the draft document nor has it yet been signed off.
Mr Tusk represents the leaders of the other 27 EU members, who all need to agree for there to be a move to the next phase of talks.
The UK voted for Brexit last year and is due to leave in March 2019, but negotiations have been deadlocked over three so-called separation issues.
The EU says it will only recommend the start of talks about future trade arrangements when it deems "sufficient progress" has been made on three issues - the status of expat citizens, the "divorce" bill and the Northern Ireland border.
The UK has been set a deadline of this week to come forward with an improved offer on the terms of the UK's withdrawal.
Mr Davis said he hoped the EU would give the green light for discussions on their future relationship with the UK at a summit on 14-15 December.
"I think this is an important day," he said before leaving for Brussels. "Everybody understands the decision to move on to trade talks is vital - it's vital for everybody. It's of huge value to the 27 members and to ourselves."
On the "divorce bill", the UK is understood to have recently increased its offer, which could be worth up to 50bn euros (£44bn).
On the issue of EU citizens' rights, it has been reported that the UK has agreed that the three million citizens from other EU states who want to stay in the UK will not have to pay to apply for settled status.
Ministers have already suggested people legally resident in the UK before an as yet unspecified cut-off date will be allowed to stay and they want to make the process "as easy as renewing a driving licence".
Progress in other areas has led to attention being focused on the Ireland question in recent days.
The Irish government is seeking guarantees from the UK that there will be no customs checks on the border with Northern Ireland after Brexit and movements of goods and people will remain seamless.
Mr Tusk has stated Dublin must be satisfied there will be no return to a "hard border" and as Irish ministers met on Monday, it seemed there was yet to be a resolution.