So far, 4,070 students from across the EU have been accepted to study in Scotland, an increase of 10 per cent compared to the same time last year.
The rise is important because EU students compete for the same places as Scots and the estimated £80 million cost of educating them is the responsibility of the Scottish taxpayer.
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However, the figures from the Universities and Colleges Admissions Service (Ucas) show no signs that Scots are being pushed out with record numbers already accepted.
Nearly 26,600 Scottish-domiciled students have secured a place to study in Scotland - an increase of four per cent compared to 2013.
A spokeswoman for Universities Scotland, which represents university principals, said: "These students compete with Scottish peers - but it's important to keep the increase in perspective.
"The increase in EU students is dwarfed by increased numbers of Scots placed this year which is close to three times the increase of EU students we have seen."
The Ucas figures also show a three per cent increase in the number of fee-paying students from the rest of the UK (rUK) getting a place in Scotland.
These students do not compete with Scots for places, but the fees of up to £9,000 a year they pay are increasingly important to the sector.
The Universities Scotland spokeswoman welcomed the increase, adding: "The cross border flow of students, in any direction, is a positive thing and a three per cent increase from England, Wales and Northern Ireland is entirely manageable."
Michael Russell, the education secretary, welcomed the record number of acceptances for Scottish students, saying: "Hundreds of prospective Scottish students have been accepted in the last week or so, which is good news."