AMs previously warned of private college regulation gaps
Concerns over the regulation of private colleges were raised by an assembly committee a year before an alleged scam at a Cardiff college was exposed.
A BBC Wales Week in Week Out reporter using fake qualifications was offered a loan to study at West London Vocational and Training College's Cardiff campus.
In 2014, the committee said there may be insufficient safeguards for private colleges based outside Wales.
Ministers said they had consulted on tightening the system since the report.
Police are talking to the Welsh government about allegations of fraud, following the undercover investigation.
Mr Lewis told AMs there was no other English-based higher education provider with a Welsh campus and it is "very unlikely that, if there is a problem here, it has spread much further afield".
He has has suspended payments to the college and says changes to the regulation system will be introduced in 2016.
In October 2014, the assembly's Children, Young People and Education Committee said it was concerned "that there may not be sufficient safeguards in respect of provision delivered within Wales by 'private' or 'alternative' providers based elsewhere in the UK".
The committee was taking evidence on the Welsh government's Higher Education Bill.
At the time, Cardiff Metropolitan University told AMs: "The Bill provides no safeguards in respect of provision delivered within Wales by 'private' or 'alternative' providers that is subsidised by the Welsh government financially."
The union Unison warned against expansion of the private sector, "especially when there is no evidence that Unison is aware of that suggests these private institutions provide the same kind of high standards as their public counterparts".
Higher education courses must be designated by the Welsh government before students can get financial assistance or help with their fees.
Mr Lewis has said he is considering introducing "more stringent criteria" for designating courses in the new year.
They would require colleges to demonstrate their status as charities, and show they are financially viable and well-managed.
On Tuesday, Mr Lewis told AMs that "we are moving towards a system in Wales which I think will give the maximum possible security around issues like this because we will be demanding that all such providers are charities".
He added: "There would be no system of regulation, or it would be difficult to contrive a system of regulation, that could be 100% proof against any planned or deliberate fraud."