Mr Davis's department said Britain's aim was to negotiate "a stable, mutual arrangement that preserves the benefits of the UK's and EU's integrated markets and recognises the unique regulatory alignment between us today".
Speaking on ITV's Peston on Sunday, she also said a customs union would be best for United Kingdom economic growth and prosperity.
Asked if she was concerned that Britain could end up with a better deal than Norway - which is not in the EU but is bound by many EU regulations as part of the European Economic Area (EEA) - Ms Solberg said that "it was not possible to have a special deal better than the EEA".
But they added "as the prime minister has already made clear, we will be leaving the single market and the customs union after EU exit day", referring to 29 March 2019.
"We have to leave the customs union to be on an equal footing with many other countries in the world so we can set our own parameters for trade".
But Ms Fairbairn will say: "There may come a day when the opportunity to fully set independent trade policies outweighs the value of a customs union with the EU".More news: 2018 survey to count the homeless in Columbus; provide them with resources
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Brexit-backing former Cabinet minister Priti Patel has urged Theresa May to ensure that the United Kingdom leaves the EU's customs union, warning that this is the only way that Britain can secure "the freedom to succeed".
Currency traders believe the mood in London and Brussels suggests both sides are more amenable to hammering out a transition agreement between Britain and the trading bloc, and then an eventual deal for the terms of departure.
"Decisions must be taken fast, or firms will have no choice but to trigger their plan Bs", she will warn. "More jobs and investment will leave our shores and future generations will pay the price".
He added: "There is no possibility, for example, to have a customs union if Britain wants to say on trade, "we want to regain our full sovereignty".
But the Foreign Secretary hit back saying: 'Staying in the customs union means effectively staying in the EU: the EU is a customs union.
Government ministers reacted furiously to previews of the CBI's evolving position over the weekend, which now directly challenges the British strategy of leaving the customs union so that new trade deals can be pursued outside a common tariff area. I voted for Leave in the belief that the United Kingdom would benefit in the longer term.