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After securing an initial agreement on Friday to move Brexit talks to a second phase, Prime Minister Theresa May is keen to start discussing future ties with the EU, and especially the type of trading agreement to try to offer greater certainty for businesses.
But despite Davis striking a confident tone, EU officials say they will only launch negotiations on a legally binding treaty after Britain leaves and becomes a "third country", according to draft negotiating guidelines.
"It's not that complicated, it comes right back to the alignment point ...
We start in full alignment, we start in complete convergence so we can work it out from there," Davis told the BBC's Andrew Marr show.
"The thing is how we manage divergence so it doesn't undercut the access to the market," he said, describing his preferred deal as "Canada plus plus plus".
But the UK economy is nearly twice the size of Canada's and British officials have said that their current alignment with EU standards and much closer trading links with the continent give them scope for an even deeper relationship.
May has been hailed by many in her deeply divided Conservative party for rescuing the agreement to unlock the Brexit talks by offering EU member Ireland and her allies in Northern Ireland a pledge to avoid any return of a hard border.
By playing with the wording, May agreed that if the two sides failed to agree an overall Brexit deal, the United Kingdom would keep "full alignment" with those rules of the EU's single market that help cooperation between Ireland's north and south.
Davis described the commitment as more of a "statement of intent" than a legally binding measure -- something that might reassure hardline Brexit campaigners who fear that it could imply that Britain was leaving the EU in name only.
Despite last week's progress, May will enjoy little respite. The second phase of talks is expected to expose the rifts in her top team of ministers over what Britain should look like once it leaves the EU.
On Saturday, environment minister Michael Gove, a Brexit campaigner, opened up the possibility of changing the terms of any agreement with the EU after Brexit if Britons felt that the deal had not reflected their demands to "take back control".
"If the British people dislike the arrangement that we have negotiated with the EU, the agreement will allow a future government to diverge," Gove wrote in a column in the Daily Telegraph.