David Willetts held 12 meetings with private education firms before publishing the white paper.
Two of the firms already face criticism in the US, where for-profit education has expanded massively in the last decade.
One of them is Apollo, which has paid out millions of dollars in fines over recruitment practices at its University of Phoenix. In 2008 the university’s graduation rate was 9 percent.
Apollo is the parent company of the private BPP University College in London.
Willetts also met with the Education Management Corporation.
The firm is being sued for more than £7 billion by the US Department of Justice over allegations of improper recruitment practices.