(BBC News) -- The fifth round of talks - the final discussions before a crucial EU summit on 19 and 20 October are due to end.
The UK has been hoping EU leaders at the summit will decide enough progress has been made to open trade talks.
The UK is set to leave the European Union at the end of March 2019.
The BBC's Kevin Connolly said there had been no indication of a breakthrough and this round of negotiations has remained "remarkably leak-proof".
EU sources have described a "constructive mood" without real progress and nothing has been said that suggests a sense of gathering momentum, our correspondent added.
Both EU and UK teams have said the ball is in the other side's court this week - implying that it is the other side that has to make the next concession.
The EU has said it wants "sufficient progress" on issues including a financial settlement, citizen's rights and the Northern Ireland border with the Republic of Ireland before the talks move on to trade.
Earlier this week, European Council President Donald Tusk warned that if the current "slow pace" of negotiations continued the UK and the EU would "have to think about where we are heading".
He suggested that the green light to begin talks about a post-Brexit trade deal would not come until December at the earliest.
Last month Prime Minister Theresa May used a speech in Florence to set out proposals for a two-year transition period after the UK leaves the EU in March 2019, in a bid to ease the deadlock.
Mr Davis has since said "decisive steps forward" have been made - although Mr Barnier has said there are still "big gaps" between the two sides on some issues.
Conservative MP Kwasi Kwarteng, Parliamentary aide to Chancellor Philip Hammond, played down reports of a cabinet row over whether money should be spent now on preparing for Britain's exit from the EU without a trade deal.
He told BBC Radio 4's Today programme there were "slight differences of opinion" but the government is "going to be prepared for every eventuality".
Labour's Hilary Benn, chairman of the Commons Brexit committee, said it would be "a disaster for Britain if we ended up with no deal" and talk of the UK being relaxed about that "I don't think convinces anyone".
He urged ministers to stop arguing amongst themselves because the "clock is ticking".
"All the signs coming from Brussels are that when the European Council meets, it will say, I'm sorry there hasn't been enough progress," he added.