The Brexit Secretary will publish five position papers further setting out Britain's negotiating strategy next week in an attempt to add pace to the talks.
A key document is expected on the Government's favoured approaches to enforcing rights outside the jurisdiction of the European Court of Justice (ECJ).
Disagreement over the ECJ's role was a major sticking point during July's round of talks, with the UK aghast at Brussels' insistence that EU citizens' rights should be enforced by the court after Brexit.
Next week's paper will set out different possible approaches to end the "direct jurisdiction" of the ECJ but still enforce individuals' and businesses' rights after Brexit.
But first, a document on goods will emphasise the Government is seeking a deal to ensure the freest and most friction-less trade possible in goods and services.
At present, the EU's position is that only goods should be discussed in "phase one" of the negotiations, in which "sufficient progress" must be made before talks on a future trade deal can begin.
But Britain believes the goods and services sectors are impossible to separate and so wants to discuss them together.
Mr Davis said: "With the clock ticking, it wouldn't be in either of our interests to run aspects of the negotiations twice."
He went on: "This week we set out more detail of the future relationship we want with the European Union, putting forward imaginative and creative solutions to build a deep and special partnership with our closest neighbours and allies.
"In the coming days we will demonstrate our thinking even further, with five new papers - all part of our work to drive the talks forward, and make sure we can show beyond doubt that we have made sufficient progress on withdrawal issues by October so that we can move on to discuss our future relationship."
Another position paper on confidentiality will make clear the Government's intentions on ensuring official documents and information exchanged between the UK, EU and other member states remain protected after Brexit.
A document will also be published on civil judicial co-operation to reassure the domestic legal sector and with an eye on August's talks.
And a paper on data will seek to ensure that it continues to be passed between the UK and EU without disruption.
Writing in the Sunday Times, Mr Davis said some early discussion of the future trading relationship would help progress on the Irish border, a key issue in phase one of withdrawal talks.
"It is simply not possible to reach a near final agreement on the border issue until we've begun to talk about how our broader future customs arrangement will work," he said.
"Furthermore, if we get the comprehensive free trade agreement we're seeking as part of our future partnership, solutions in Northern Ireland are easier to deliver."
Meanwhile, Sir Paul Jenkins, who was the Government's most senior legal official for eight years until 2014, said Britain would have to replicate EU rules and submit to the ECJ "in all but name" if it wants to remove the need for hard borders.
Last week the Government published a paper setting out its wish for close customs arrangements with the EU and no hard border between Northern Ireland and the Republic of Ireland.
"If the UK is to be part of something close enough to a customs union or the single market to remove the need for hard borders, it will only work if the rules are identical to the EU's own internal rules," Sir Paul told the Observer.
"Not only must they be the same but there must be consistent policing of those rules. If Theresa May's red line means we cannot be tied to the ECJ, the Brexit treaty will need to provide a parallel policing system.
"That may be a new court but, in reality, any new court will have to follow what the ECJ says about the EU's own rules, otherwise the new system won't work. So, never mind Theresa May's foolish red line; we will have the ECJ in all but name."
Liberal Democrat Brexit spokesman Tom Brake MP said: "David Davis promised us 'the row of the summer' over the Brexit timetable, only to capitulate weeks later to the EU's preferred timetable after a disastrous general election for his party which vastly undermined their negotiating position.
"To be now, a couple of months down the line, trying to reopen the issue reeks of desperation at an approaching economic storm and a Cabinet who don't have a clue.
"Constant reports of Cabinet spats show our Government cannot even agree a position between themselves, let alone win concessions from EU negotiating teams in our country's best interests."