The study by the Higher Education Policy Institute, published on 5 May, also suggests that private institutions could be given greater access to libraries, sports facilities and social centres operated by publicly funded universities to make treatment of the two sectors more "equitable".
Both ideas would ideally run alongside a complete overhaul of the regulatory framework governing private providers in a bid to slim down the "multiple accreditations and reviews" that many are subject to, it adds. In one case cited, a private provider was involved with 39 accrediting bodies.
The report, Private Providers in UK Higher Education: Some Policy Options, suggests that in return for more public funding, private colleges should be subject to a more uniform and transparent regulatory regime.
One option would be to ensure that all institutions - publicly funded and private - were accountable to a single "risk-based" accreditation system so that the entire sector faced the same checks.
The study also suggests that corporate providers - and foreign institutions that set up in the UK - be asked to obtain licences to operate as higher education businesses.
The authors of the report - Robin Middlehurst, professor of higher education at Kingston University, and John Fielden, who leads university consultancy firm CHEMS Consulting - say that the "case had been made" for the government to address anomalies affecting private bodies in areas such as immigration, tax and quality assurance.
"The present mix of regulations has developed over time as a result of ad hoc responses to particular political or educational drivers. There is no comprehensive framework," they say.
The study suggests that an essential part of a regulatory overhaul would be the requirement that all private providers submit official data so that statistics on staff and student numbers, financial accounts, ownership and governance were transparent and widely available.
It adds that, provided adequate safeguards were in place, there is no reason why the private sector should not be treated in a fairer manner and given access to public funds for teaching and even research.
The report considers the option of opening up the "academic resource infrastructure" to private providers willing to make the "appropriate payment", with the state contributing to the cost of mergers or takeovers involving failed universities. It also suggests that properly regulated private colleges be made exempt from charging VAT on fees - as is the case with traditional universities.
On research, the report states that "there may be a case for opening up public funding" to applications from private staff.
However, Professor Middlehurst and Mr Fielden (who also published an extensive report on the private sector for Universities UK last year), sound a warning. If regulation were not carefully implemented, they say, there is a danger of the UK repeating the mistakes of the US system - where some for-profits have been accused of misleading students.
This, they add, is due to the fact that the growth in US for-profits has been built on access to state-sponsored student loans - something already happening in the UK, albeit on a much smaller scale.