He suggests the British government's task will be to stop the border "becoming significantly harder"
The British Foreign Secretary Boris Johnson appears to have told the UK Prime Minister Theresa May "it is wrong to see the task as maintaining 'no border'" on the island of Ireland after Brexit.
He says the British government's task will be to "stop this border becoming significantly harder".
The leak from the UK cabinet's Brexit deliberations on the border is included in a letter passed to British broadcaster, Sky News.
Writing to Mrs May, Mr Johnson also seeks to play down the "exaggerated impression" of "how important checks are" at EU external borders.
He also goes as far as contemplating a hard border between Northern Ireland and the Republic of Ireland, writing: "Even if a hard border is reintroduced, we would expect to see 95% + of goods pass the border [without] checks."
It suggests a significant downgrading of expectations about the change to the border as a result of the UK government's Brexit strategy and Mrs May's plan to leave the EU's single market and customs union.
As recently as November last year, Mr Johnson told the UK House of Commons: "There can be no return to a hard border. There can be no hard border.
"That would be unthinkable, and it would be economic and political madness".
In February 2016, ahead of the EU referendum, Mr Johnson promised the Irish border would be "absolutely unchanged".
The document is Mr Johnson's response to Mrs May asking him to substantiate a claim made at a meeting on February 7th, when talks centred on Northern Ireland and immigration.
Referring to the meeting in his letter, Mr Johnson wrote: "I offered, and you [the Prime Minister] agreed, to send you a paper setting how I believed the Ireland/ NI border issues could be managed on the basis of a highly facilitated solution."
The letter, entitled "The Northern Ireland/Ireland border - the Facilitated Solution", accompanies a "concept note" that "draws on UK Foreign Office expertise".
This appears to be an attempt to meet commitments given by Mrs May to the EU as part of the first phase of Brexit negotiations, before an agreement was reached in December last year.
Then, she undertook that, post-Brexit, there would be no hard border between Northern and Ireland and the Republic of Ireland.
In the note, officials appear to have distanced themselves from the conclusions of Mr Johnson, stating at the top of the paper: "It is an FCO concept note based on discussion with other departments but is not agreed technical advice".
The thrust of Mr Johnson's point to Mrs May is that there already is a border on the island of Ireland, so it is "of course a fallacy" that Brexit will see a border re-emerge.
Mr Johnson says British Revenue and Customs "only" checks 4% of consignments arriving in the EU at the UK's external border, and other authorities only 1%.
He claims "in short the EU border is already largely a border" that relies on electronic paperwork and "not physical inspection".
But the figure quoted is believed not to take into account the much higher level of checks required on agricultural and food trade across that border, in a situation where regulations and standards have diverged.
Earlier Mr Johnson was criticised for comparing the Irish border to travelling between different boroughs in London.
The leak comes on the eve of the publication of a draft legal text from the phase one Brexit agreement, agreed by EU27 officials.
It is likely to focus on the "backstop option" of "full alignment" of Northern Ireland with the rules of the EU's customs union and single market, in the absence of a Brexit deal.
The legal text of a deal to avoid a hard border with Northern Ireland is due to be published on Wednesday.
The Irish Government are satisfied with the text agreed on in Brussels, and say it will avoid any return of a hard border with Northern Ireland.
How this will happen remains to be seen.