The latest log of external meetings published by the Department for Business, Innovation and Skills shows that in May the universities and science minister met with Exponent Private Equity, Duke Street, Providence Equity Partners and Silverfleet Capital "to discuss higher education".
Exponent and Providence have been linked in media reports with takeover bids for The College of Law, a not-for-profit private institution with degree-awarding powers.
Times Higher Education has reported predictions from Glynne Stanfield, a partner in the education group at Eversheds, that a private provider or private equity firm would buy a higher education institution in whole or part "within six months".
By buying a higher education institution in whole, a for-profit private firm would take control of its degree-awarding powers - with the potential to expand the range of degrees.
The College of Law was present at the meeting with Mr Willetts, as were for-profit private providers Pearson - also reported to have an interest in taking over the college - and Kaplan Europe.
The meeting took place at a dinner organised by Hawkpoint, a corporate finance advisory firm that specialises in mergers and acquisitions.
A BIS spokeswoman said: "This was an event with a wide range of attendees where a variety of issues relevant to higher education were discussed."
In December 2010 and January 2011, Mr Willetts met with the private equity firm Warburg Pincus to discuss higher education.
BIS recently closed a technical consultation on the sector's regulatory framework that canvassed views on whether it "would be helpful to institutions to ease their ability to convert to a legal status of their choosing - for example, to make it easier for them to attract private investment".
The consultation response by the Higher Education Funding Council for England, also present at the Hawkpoint meeting, says that "were changes of legal status to occur, a challenge would relate to the fact that most higher education providers have charitable status and are therefore subject to charity law.
"A charity's assets must be applied to its charitable purposes, whether or not a change in legal status has taken place."
That belief may be tested if a private for-profit body were to buy The College of Law, a charity with a Royal Charter.
Pearson, which recently said it would raise £450 million by selling its 50 per cent share in FTSE International, has experience of buying a charity after taking over exam board Edexcel.
Also at the Hawkpoint meeting was Greenwich School of Management, a private institution majority owned by private equity firm Sovereign Capital. Among other attendees were training firms including A4e, whose higher education courses for the unemployed will be validated by Glyndwr University.