Writing for the Daily Telegraph, the remain-backing Finance Minister Philip Hammond and the Eurosceptic Trade Minister Liam Fox said Britain would leave the European Union in March 2019, there would be a short "interim period" to smooth the transition during which Britain would not be party to European Union treaties and after that Britain would become fully independent.
The two ministers, who represent the Remain and Leave wings of the Tory party respectively, write that Britain will not stay in the European Union by the "back door".
"We've been crystal clear that issues around our withdrawal and our future partnership are inextricably linked, and the negotiations so far have reinforced that view", a source in Britain's Brexit department said.
Over the coming 10 days, a number of Government papers will be published spelling out the UK's Brexit blueprint on key issues including the customs union, the Irish border, fisheries and agriculture.
"These papers show we are ready to broaden out the negotiations", the source said.
In July, EU officials said progress was hard not because Britain had unacceptable demands, but because it had no position at all on many issues.
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.
The Sunday Telegraph reports one proposal will involve offering Irish citizens free movement in and out of the UK.
"But we are also clear that during this period our borders must continue to operate smoothly; goods bought on the internet must still cross borders; businesses must still be able to supply their customers across the European Union and our innovative, world-leading companies must be able to hire the talent they need, including from within the European Union".
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.
The British ministers also promised a series of papers on their ideas for a "Future Partnership" with the EU to be presented in the run-up to October's European Council. The first will be a proposal for new customs arrangements.
Writing in the Sunday Telegraph, Mr Hammond and Mr Fox said the United Kingdom definitely will leave both the customs union and the single market when it exits the EU in March 2019.
Prime Minister Theresa May formally triggered the Brexit process on March 29 and divorce negotiations officially began on June 19.
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.