Tom Harris, a former MP who now heads the Vote Leave campaign in Scotland, said he wanted higher education institutions north of the border to be able to give Scots wanting to go to university “preferential treatment” when awarding places.
At the moment, European laws prevent that from happening, with universities required to treat applicants from Scotland and the rest of the EU equally.
Mr Harris, speaking at the launch of the Vote Leave campaign in Scotland, said: “I would much rather give preference to Scottish candidates and force people from anywhere out the UK to pay tuition fees. It’s quite difficult to argue against that.
“If my kid applies to university and someone from Poland applies to the same course, we can’t differentiate between those two applications, we can’t say ‘one’s from Scotland, therefore we’re going to give him preferential treatment’, that’s illegal.
“I actually think we should give Scots preferential treatment.”
Mr Harris added statistics showed the number of Scottish students accepted to Aberdeen, Glasgow, Edinburgh and Dundee universities had fallen in the past two years while at the same time an increasing number of Europeans had been awarded places.
He said: “It doesn’t have to be this way. EU law prevents universities from distinguishing between Scottish and EU students.
“EU students compete for the same places as Scottish students, meaning Scottish students often end up missing out on funded places at our universities.
“If the UK left the EU, Scotland would be free to set a new policy on EU applicants.
“They could be charged the same fees paid by other UK students, bolstering the finances of our universities, thereby securing free university tuition for Scottish students for the long-term.”
Mr Harris also argued leaving the EU would make the Scottish Parliament more powerful, saying in the event of a Brexit vote Holyrood would take responsibility for policy in any areas that are not specifically designated as being reserved to Westminster under the Scotland Act.
Scotland would also be £1.5 billion better off, Mr Harris said, stating this is how much the country contributes to the amount the UK pays to Brussels each year.
He made the comments as Vote Leave launched its Scottish campaign at a visit to White House Products in Port Glasgow, Inverclyde, which manufactures hydraulic pumps.
The firm is owned by the Scottish chairman of the Business for Britain pressure group, Alistair MacMillan.
While polls have suggested a majority of Scots want to stay in Europe, Mr Harris said people were more open to switching their vote than they were in the 2014 independence referendum.
He said in that poll people “would go to their deaths without having changed their mind”.
But he argued in this referendum, people were more willing to listen to the arguments.
The former Labour MP, who lost his seat at Westminster last year, predicted turn-out on June 23 will be lower than the 85% record high achieved in the independence vote, saying “people just don’t feel as strongly”.