Chancellor Philip Hammond is to set out plans for Britain to stay in the single market at a meeting of Cabinet ministers this week, but is likely to face resistance from his colleagues.
According to the Sunday Times, Hammond will look for access to the single market "on a sector by sector basis" - with financial services being a top priority.
However, he is at odds with the key Cabinet ministers responsible for planning Brexit, David Davis and Liam Fox, who are keen to make sure Britain is free to impose border controls, which may be incompatible with remaining in the single market.
Top German politicians have signalled that Britain would be unable to limit free movement and gain access to the single market - but have said that the country should be awarded a "special status" following Brexit.
Prime Minister Theresa May has called on her Cabinet colleagues to put forward their plans for Brexit - and Britain's negotiations with the EU - at a meeting on Wednesday.
Both Davis and Fox want May to activate Article 50 early next year, kicking off Britain's exit from the European Union. In signs that May is also keen to start negotiations with the EU, she has reportedly been in talks with lawyers about triggering Article 50 without holding a parliamentary vote.