International Trade Secretary Liam Fox appears to have signalled that the UK could remain a partial member of the EU Customs Union after Brexit.
Remaining a full member means the UK would have to keep the same international tariffs as the European Union but it could hamper Britain's ability to cut free trade deals after its withdrawal.
In an interview on the BBC's Andrew Marr Show, Fox insisted that Brexit was not like a "boiled egg".
"I hear people talking about hard Brexit and soft Brexit, as if it's a boiled egg we're talking about."
"It's a little more complex", he said, adding: "Before we make final decisions we need to look at the costs".
In respect to the prospect of a so-called hybrid arrangement where the UK remains in the customs union and also negotiates global free trade deals, Mr Fox said: "We can't go for a quick result, we have to get the right result."
"Whatever result we do come to, we have to be able to put in front of the British people the reasoning for coming to that result."
When asked if he was personally open to Britain staying in the customs union, Mr Fox declined to directly answer, insisting he would "argue his case inside cabinet".
However, he acknowledged that he was "instinctively a free-trader".
He added: "At the moment, the only place where people are talking about imposing impediments to trade and investment which don't exist at the present time is in the European Union, and in an economy that's relatively flat, that doesn't make sense."
"We have to have a more open trading environment."
The trade secretary also said that while the UK cannot enter trade agreement negotiations while in the EU, it is "rational" to have discussions over "trade liberalisation in general and to scope out how future agreements might look like with other countries"
Mr Fox also insisted that it was importance to stress that Britain wants the European Union to be "a strong trading and economic and security partner for the United Kingdom".
"If we can come to an agreement that minimises any trade barriers it's good for the people of Europe," he added.
When asked if he thought the Article 50 formal withdrawal process would be revocable once triggered, Mr Fox said "it's not a matter of legality it's a matter of democracy".
He added: "As we get in 2017, I hope that people will actually accept that the public have given us an instruction.
"When people try to undermine that result, I ask myself what don't they understand about the words democracy, referendum or binary."