The UK has set out the "ambitious new customs arrangement" it wants to secure with the EU after Brexit, reports the BBC.
Ministers said the plans would mean the "freest and most frictionless possible trade" with the rest of Europe.
This could include a "temporary customs union" after Brexit to prevent border problems as the UK leaves the EU.
Businesses have called for clarity since the UK said it was leaving the customs union - the EU's tariff-free trading area - as part of Brexit.
The customs union document is the first of a series of papers to be published by the UK government on key negotiation issues.
On Wednesday it is expected to set out proposals for the border between Northern Ireland and the Republic of Ireland.
What is the customs union?
Countries in the customs union don't impose tariffs - taxes on imports - on each other's goods.
Every country inside the union levies the same tariffs on imports from abroad.
So, for example, a 10% tariff is imposed on some cars imported from outside the customs union, while 7.5% is imposed on roasted coffee.
Other goods - such as soap or slate - have no tariffs.
The UK's departure from the EU's customs union was confirmed at the weekend in a joint article by Chancellor Philip Hammond and Trade Secretary Liam Fox.
A 'streamlined' border
According to the newly-published government paper, the UK could ask Brussels to establish a "temporary customs union" after it leaves the EU in March 2019.
But during this period, it would also expect to be able to negotiate its own international trade deals - something it cannot do as an EU customs union member.
Once this period expires, the UK will look to agree either a "highly streamlined" border with the EU, or a new "partnership" with no customs border at all.
Brexit Secretary David Davis (left) and the EU Commission's Michel Barnier are leading the negotiations for the two sides
The government said the interim arrangements would mean businesses would only have to adjust once to the new arrangements.
All of this will have to be negotiated with the EU - and the two sides have not yet even started discussing trade matters.
Other obstacles - including the size of the UK's "divorce bill" - need to be agreed first.
Brexit secretary's view
David Davis, Secretary of State for Exiting the European Union, said he envisioned the interim customs system being "as close as we can to the current arrangements", but with the UK able to negotiate and sign its own international trade deals.
Speaking on BBC Radio 4's Today programme, he did not rule out the UK paying to be part of the arrangement, saying he was not going to conduct negotiations on air.
And he said he did not believe the European Court of Justice would be the arbiter of the temporary arrangement, adding that the government would publish proposals on "international arbitration" next week.
Mr Davis businesses were worried about "the infamous cliff edge" - the UK leaving the EU without replacement trade and customs deals.
He added that the period should be "something like two years, maybe a bit shorter" but said the transition period had "to be done by the election", which has to take place by 2022 at the latest.
What the EU says
A European Commission spokesman said: "We will now study the UK position paper on customs carefully in the light of the European Council guidelines and the council's negotiating directives.
"The next negotiation round will start in the week of 28 August.
"We take note of the UK's request for an implementing period and its preferences as regards the future relationship, but we will only address them once we have made sufficient progress on the terms of the orderly withdrawal.
"An agreement on a future relationship between the EU and the UK can only be finalised once the UK has become a third country.
"As Michel Barnier has said on several occasions, 'frictionless trade' is not possible outside the single market and customs union."
The EU is also working on a position paper on the customs union.
Mixed UK reaction
Keir Starmer, Labour's shadow Brexit secretary, said the proposals were "incoherent and inadequate" and were designed to "gloss over deep and continuing divisions within the cabinet".
"These fantastical and contradictory proposals provide no guidance for negotiators or certainty for businesses," he added.
Labour MP Keir Starmer said the plans were "fantastical"
Liberal Democrat Brexit spokesman Tom Brake said the plan would "only delay the economic pain caused by leaving the customs union".
"We still face the prospect of more red tape for businesses, longer queues at our borders and higher prices for consumers once the transition comes to an end."
However, the CBI, which represents British businesses, said the proposal was "encouraging".
Its deputy director general, Josh Hardie, added: "The clock is ticking and what matters now is giving companies the confidence to continue investing as quickly as possible."
Adam Marshall, director general of the British Chambers of Commerce, said most businesses were more concerned about future customs arrangements with the EU than future trade deals.
"In the long term, we should aim to avoid imports and exports being subjected to two sets of customs checks, and to ensuring the smoothest possible future trade relationship between the UK and EU."
MEP and former UKIP leader Nigel Farage attacked the idea of a transition, tweeting: "I warned of the great Brexit betrayal two weeks ago. It is now official government policy."
Analysis: UK 'hustles' Brussels
Adam Fleming, BBC Brussels reporter, said the UK was seeking a customs union agreement "that will keep things broadly the same for an interim period - an attempt to reassure business".
"Firms will be told they'll only have to change their processes once," he said.
"In Brussels, EU negotiators are likely to stick to their position that that the future relationship can't be considered until agreement has been reached on their priority issues - the rights of citizens, a financial settlement and the Irish border."
BBC political correspondent Ben Wright said the UK government was "straining to show that it does have a route-map for Brexit".
He said ministers were also attempting to "subtly" put the issue onto the negotiating table sooner than Brussels wants.
"They want to hustle EU negotiators into talking about trade much sooner than Brussels intends," our correspondent said.