It suggests the Government wants to "have cake and eat it" but this would be difficult given the attitudes of the French negotiation team.
The document was spotted in the arms of the chief of staff to Mark Field, the vice-chairman of the Conservative party, as he left a meeting at the Department for Exiting the European Union on Monday.
The document also says the triggering of Article 50, which formally starts Brexit negotiations, was likely to be "difficult". It reveals that the EU's chief negotiator, Michel Barnier, "wanted to see what the deal looks like first" but the Government does not want to provide details.
It says Britain wanted to have a "Canada plus" trade deal rather than remaining a member of the European Economic Area (EEA) but negotiating over services, especially the financial sector, is likely to be "difficult".
The notes also suggested Britain would no longer under the jurisdiction of the European Court of Justice.
The memo comes after many complained the Government appeared to have "no plan" for Brexit as they have yet to lay out a definitive negotiating strategy.
Pro-EU think-tank British Influence is writing to Brexit Secretary David Davis to seek clarification on the Government's position regarding the UK's status in the wider European Economic Area (EEA) when it quits the EU.
The think-tank has said a legal challenge is likely as it believes leaving the EU does not mean quitting the EEA which extends the single market's tariff-free trade in goods to countries like Norway, Iceland and Liechtenstein.
A legal challenge could result in Parliament being given the final say on EEA membership.
A spokesman for British Influence said: "It is likely there will be a legal action because, in our view, the Government has taken a stance that leaving the EU means leaving the single market."
Campaigners argued that it would be undemocratic for the Government to effectively repeal the European Communities Act 1972 without the consent of Parliament and there needed to be proper parliamentary oversight of the Brexit process.
The case is due to be heard in the Supreme Court before Christmas but could then be taken to the European Court of Justice.
A Government spokesman said: "These individual notes do not belong to a Government official or a special adviser. They do not reflect the Government's position in relation to Brexit negotiations."
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies
Join our commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies