In an embarrassment for ministers, the paper suggests that even top universities, including members of the prestigious Russell Group, struggle to justify £9,000 fees for all courses.
It goes on to say that teaching on some courses charging the top rate is less intense and less effective than lessons at the best-funded state schools, despite similar costs.
The memo was being held by an aide on Downing Street on Monday when it was snapped by a press photographer.
What the paper says
[The Department for Business, Innovation and Skills (BIS)] are due to publish an HE (higher education) White Paper alongside the Queen’s Speech and introduce the planned 2nd session bill shortly afterwards.
BIS are trying to solve real problems of quality and regulation. But it is not clear they have figured out how - and theres is a risk that the bodies and rules they will establish in legislation will not solve teaching quality, while creating poor quality provision for marginal students.
What problems is the Bill trying to solve?
[Obstructed] Education across the spectrum - from some in the Russell group to courses [obstructed] through FE colleges - do not offer the quality and intensity of teaching we expect for 9k.
This is the same funding as some of the best-funded state [obstructed] in England, which offer far more intensive teaching and are able to show [obstructed] in outcomes.
In a further revelation, the paper says that the government's pledge to double the number of young people going to university from disadvantaged backgrounds "will not be achieved".
It says that a combination of high entry requirements and reluctance to expand means established institutions alone will not help achieve its aim.
Instead, the government hopes new institutions and providers will better serve disadvantaged groups.
The Coalition pledged to radically reform higher education in 2010 and outlined plans to raise the cap on tuition fees in England from 2012 up to £9000.
At the time, ministers said that the move would lead to an "increased focus" on teaching quality.
The leaked memo reveals that the Conservative government believes this has not transpired, The Daily Telegraph reported.
It says ministers are considering "sensible" regulation to ensure teaching standards are met.
“This leak is a shocking admittance of failure”
Gordon Marsden, Labour’s shadow minister for universities, told The Daily Telegraph: "This leak is a shocking admittance of failure and shows what ministers really think of David Cameron’s flagship policy.
"The Government seem content to throw in the towel on efforts to widen participation in the existing higher education system, meaning that students from the least well-off families will be left behind."
The Russell Group said that students at leading universities consistently reported high satisfaction.
A BIS spokesman said: "The rate of entry for disadvantaged students to university is at a record high and we are committed to ensuring that everyone with the potential has the opportunity to benefit from higher education, regardless of their background."