The UK could seek a deal which would allow sections of the economy to remain within the EU's customs union after Brexit, international trade minister Greg Hands has suggested.
Mr Hands said officials would be able to choose the type of products to be covered by agreements.
The union operates alongside the EU's single market and free trade area.
It comes after the Brexit secretary said the UK would consider paying for "best possible" single market access.
The customs union includes all 28 EU nations, but also Turkey, Monaco, San Marino, Andorra and non-EU UK territories such as the Channel Islands.
They enjoy free trade with each other, but must impose the same tariffs on goods from nations outside the pact and are barred from doing bilateral trade deals with other countries.
Bloomberg news agency published remarks Mr Hands made in an interview this week in which he said the "history of international trade has got all kinds of examples of customs unions".
He said the UK could be selective about which individual sectors it wished to be covered by any customs union arrangement.
Mr Hands added: "You can choose which markets, which products the customs unions affect and which they don't, so there isn't a binary thing of being inside the customs union or outside of the customs union."
As the pound posted its fifth consecutive week of gains against the euro, Mr Hands's words were cited by financial market commentators as further evidence that fears over a "hard Brexit" were easing.
In the Commons on Thursday, Brexit Secretary David Davis had said the "major criterion" was getting the best access for goods and services to the European market.
Later, in a speech to CBI Wales in Cardiff, Mr Davis sought to reassure business leaders that immigration controls after Brexit will not be imposed "in a way that it is contrary to the national and economic interest".
But Brexit-backing Tory MP Peter Bone said "people would be absolutely outraged" if the UK continued to pay the EU after Brexit.
And another prominent Leave campaigner and former Conservative cabinet minister, Iain Duncan Smith, told the BBC he believed Mr Davis had been simply not ruling anything in or out of the government's Brexit negotiations.