The Committee of Scottish Higher Education Principals believes the latest application figures may show tuition fees are not deterring potential students.
Coshep says the most recent figures from the Universities and Colleges Admissions Service indicate applications are particularly low from the bottom three social classes, who are almost certainly exempt from paying fees.
"The figures we have suggest that it may be the scrapping of maintenance grants and not the introduction of tuition fees which is having the real effect," said Coshep secretary Ronald Crawford.
But the National Union of Students Scotland has strongly opposed Coshep's argument. A spokesman said: "You can't say tuition fees have no deterrent effect. The fact that people know fees are out there can in itself be a deterrent. I think it is quite clear fees are going to deter people who fear their families will have to pay and aren't sure whether they are exempt."
Coshep says the Scottish Parliament's forthcoming inquiry into student support must closely examine tuition fee exemption levels. It points to an above average drop in applications from social class II, where families are likely to be liable for some contribution to fees, but where salaries may not be particularly high.
"With a summer-long inquiry into student support ahead of us, it is essential that we have all the information we can get. We will be calling on UCAS to help provide the figures which will allow us to get the best deal for students," Dr Crawford said.
Coshep repeated its concerns to Henry McLeish, Scotland's new minister for enterprise and lifelong learning, during the Scottish Higher Education Funding Council's annual sector conference this week. Mr McLeish said he hoped the review team's membership and remit would be announced in the next fortnight.
"We want to take the question of tuition fees and put it into the context of student funding. It is about widening access, attracting more young people and adults from socially excluded backgrounds," he said.
He and the Liberal Democrat deputy minister, Nicol Stephen, predicted that the review would draw on international experience.
Mr Stephen said: "I think we have got to look at what happens in other countries. That should be part of the review.
"An interesting thing in the context of the new Scottish Parliament is that you can already sense that the discussions and approach are starting to look more to international comparisons."
Coshep expects a senior academic or higher education official to be appointed to the review team.