The prime minister’s advice, revealed in a letter between their two offices obtained by The Times, may signal Mr Cameron’s awareness that the government’s immigration policy has had a negative impact on universities.
The letter was sent by Simon Case, the prime minister’s private secretary, to Holly White, the universities and science minister’s senior private secretary.
Mr Cameron’s apparent advice to Mr Willetts in the letter to help open up academies and free schools to fee-paying overseas students was reported today by The Times.
However, the full letter also contains advice on higher education policy not reported by the newspaper.
“We should…seek to encourage more foreign universities to set up in the UK – as the prime minister has discussed with your minister on a number of occasions,” Mr Case tells Ms White.
Such a policy direction could raise anxiety among UK universities, who are likely to fear that foreign universities on their doorstep will bring increased competition for overseas and home students.
On international students, the letter says that “we need to pitch our offer to international students more persuasively. Is there a way we can bring together the ‘UK offer’ into an easily understood package?”
The letter urges Mr Willetts’ office to work with the Home Office “to identify targeted ways in which we can use our student visa offer to attract the brightest and the best”.
“Options could include, for example, giving PhD students in STEM subjects only a three-year wait before they can apply for citizenship rather than the normal five years,” the letter says.