The Brexit Secretary told MPs that ministers want to "get the best possible access for goods and services to the European market" after the UK has left the bloc and suggested the Government is open to the possibility of making contributions to the EU to secure that access.
It is the first time a Government minister has openly signalled that money could be handed over to Brussels to secure favourable trading terms with the continent.
Meanwhile, Hilary Benn, the Labour chairman of the Commons Brexit Committee, has urged the Government to publish details of its negotiating plans as he said MPs were "fed up" at the lack of detail.
The disclosure from Mr Davis regarding the possibility of continued access to the single market came in response to a question from Labour MP Wayne David (Caerphilly).
David asked during Brexit questions in the Commons: "Will the Government consider making any contribution in any shape or form for access to the single market?"
Davis replied: "The simple answer we have given to this before is, and it's very important because there is a distinction between picking off an individual policy and setting out a major criteria, and the major criteria here is that we get the best possible access for goods and services to the European market.
"If that is included in what you are talking about then of course we would consider it."
Mr Benn asked Mr Davis when the Government will set out its Brexit blueprint as he highlighted growing frustration amongst MPs.
He said: "In a week in which it has been reported that the Foreign Secretary has told EU ambassadors that he doesn't agree with the Government's policy on freedom of movement and that a Dutch member of parliament attended a briefing in Downing Street on the Government's plans for Brexit, does the Secretary of State understand why the House is getting a little fed up with being told nothing?
"If he does, can he tell us when the Government will come forward with its plans for Brexit including on what will happen as regards any future contributions to the European Union after we have left?"
Davis said he is due to appear before the Brexit committee in December and that members of the committee had visited the Department for Exiting the EU.
He said: "But you also know full well as a previous international development secretary, as a previous cabinet minister, that the approach to this, the probable success of the negotiations depend very greatly on us being able to manage the information and keep what needs to be secret until the last minute secret.
"In terms of the other things you talked about this week, frankly, this is all based on a presumption that a scribbled note in Downing Street actually is anything like Government policy. It wasn't."
Labour former shadow health secretary Heidi Alexander told Mr Davis "we are no further forward with a plan to leave the EU than we were five months ago".
She asked: "Can the Secretary of State tell me when the Government is going to drop the pretence that Brexit can mean continued tariff-free access to the single market and an end to freedom of movement?
"Don't the British public deserve better than this embarrassing charade?"
Davis said the triggering of Article 50 was still "four to five months" away and that when negotiations begin the Government's position will be "very clear".
Davis also suggested the UK would consider a transitional arrangement with the EU, adding that he wanted Brexit negotiations and new trade rules to be in place within two years of triggering Article 50.
Labour's Emma Reynolds, a member of the Exiting the European Union select committee, asked Mr Davis if he would consider a transitional deal with the EU as part of the UK's exit strategy.
In reply, Davis said: "We are seeking to ensure a smooth and orderly exit from the European Union, and it would not be in the interests of either side, Britain or the European Union, to see disruption.
"To that end, we're examining all possible options, focusing on the mutual interests of the UK and the European Union."
Reynolds pressed Mr Davis on this, warning about what would happen if British business was forced "off that cliff onto WTO rules and tariffs".
Davis responded: "We want to see a smooth, orderly exit.
"How that occurs will be affected by a number of things. She mentioned the structural issue of how the negotiation is being done, in terms of whether it's done in parallel or in series.
"We don't accept the in series approach, in terms, we've made that plain to the European Union and we need to deal with that before we come to the detailed question of whether there's transitional or not."
He added: "Transition, when it's raised by various people, will mean different things.
"For example, at least one of the Europeans talking about this has effectively meant a much, much longer negotiation period, whilst other people are concerned about matters such as financial stability.
"They're different issues that need to be dealt with in different ways."
Earlier in the debate, Labour's Pat McFadden, another select committee member, asked Davis whether the Government planned on negotiating Brexit and its new terms of trade within two years of triggering Article 50.
In reply, Davis said: "The answer is yes, we want to see them both done in parallel inside the two years."
Davis also said many in the EU had not accepted that Brexit would happen, after the SNP's Patrick Grady (Glasgow North) used the phrase "if the UK finally leaves".
Davis said: "There's no if about it, there's a when, and I say this to him quite firmly, because this is part of the problem the European Union has had in engaging on this process so far.
"So many of them want to see this not happen, and they have to face up to that so we get the right answer."
Davis also defended Foreign Secretary Boris Johnson, amid reports he privately supports free movement of people after Brexit.
Davis told MPs: "What I've seen in the papers this morning strikes me as completely at odds with what I know about his (Mr Johnson's) approach to this matter.
"He believes very clearly, and he made this clear in the Leave campaign, because he was a much more major part of it than I was, he believes that some immigration is useful.
"We all agree that. That is not the same as thinking that free movement of people, as it now stands, is a good idea. It's a problem."
However, shadow Brexit secretary Keir Starmer said comments from Mr Johnson and leaked documents risked damaging the Brexit negotiations.
"The Prime Minister and the secretary of state have repeatedly said there will be no running commentary on their Article 50 plans," said Mr Starmer.
"Yet there is a running commentary. It's being provided by leaked memos, notes caught on camera, and the near-constant comments from the Foreign Secretary to anyone who will listen to him.
"This is serious, because it is damaging the prospects of the negotiations getting off to a good start.
"The secretary of state must realise that this is going to continue throughout the two years, unless and until he discloses the basic plan the Government is adopting to this House."
In reply, Mr Davis said the Government had already set out its strategic aims and that Government did not want to cut down its options.
He added: "The dominating factor here is not what's in the newspapers.
"The dominating factor here is what's the best outcome for Britain in the long run."
Asked about Davis' suggestion that Britain could continue paying for the single market post-Brexit, Prime Minister Theresa May's official spokeswoman told a Westminster media briefing: "What he said in the House this morning is consistent with what we have said to date, which is that it will be for the UK Government to make decisions on how taxpayers' money will be spent.
"We've said, as we approach these negotiations, we want to get the best possible access for British businesses to trade with and operate within the single market, while also taking back control on immigration."
Mr Davis's response to the question of payments to the single market was merely setting out what the Government's approach would be "if people are suggesting we should consider this" during talks, said the spokeswoman, adding: "All these issues will be a matter for the negotiation."
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