That will come alongside other documents setting out how Britain's involvement in the customs union with other EU countries this week. The EU has warned that an already-tight timetable could be delayed ahead of a scheduled March 2019 exit.
Brussels has refused to start talks on a post-Brexit relationship with London until the immediate issues of Britain's withdrawal، including its "divorce bill،" have been settled.
News of the offer of a "Schengen area" between Britain and Ireland came as the Government prepares to publish a formal proposal to the European Union on the future of the Northern Irish border.
But Brussels negotiators have insisted there are three issues to be sorted before a new relationship can be discussed.
The government's Brexit department said Britain wants to show that progress on the preliminary issues has been made and "we are ready to broaden out the negotiations" by the time of an European Union summit in October.
Writing in The Observer, he said the country should have the chance to vote on any Brexit deal in a second referendum with a straight choice between remaining in the European Union and the negotiated alternative.
But in a show of strength after a summer dominated by cabinet splits, Chancellor Philip Hammond and International Development Secretary Liam Fox announced there will be a transitional period when Britain finally leaves the UK.More news: Super-sub Giroud settles thrilling Premier League opener for Arsenal
A British paper focused on "issues unique to Northern Ireland and Ireland" is expected ahead of the talks, but no further details of the proposal were provided on Sunday.
Chapman said Friday "there is an enormous gap in the center now of British politics" that could be filled by an anti-Brexit force.
Mr Davis said the publication of the papers outlining the government's aims for Brexit would mark "an important next step" towards delivering the referendum vote to leave the EU.
A second batch of papers, to be released in the run-up to the October meeting of the European Council in Brussels, will look at "future partnership" arrangements, including the UK's proposals for a new customs agreement with the EU. The first of these will set out proposals for a new customs agreement, it said.
Senior members of the Government have declared the United Kingdom will not seek to remain in the European Union "by the back door" and will leave both the single market and the customs union when Brexit happens in 2019.
Meanwhile, former Labour Foreign Secretary David Miliband has called for politicians on all sides to unite to fight back against the "worst consequences" of Brexit.