Sweden is almost certain to introduce tuition fees for students from outside the European Union within the next year.
A spokesman for Thomas Ostros, the Education Minister, said legislation was "likely" to be put before Parliament soon.
In 2003, 10,600 exchange students came to Sweden, according to the National Agency for Higher Education. But this may account for only two thirds of the total number of foreign students.
The Tidningarnas Telegrambrya news agency suggested that the figure was nearer 14,000 as many so-called free movers - students who have come to Sweden under their own steam - are not taken into account.
Helena Mähler of the research and policy division of the National Agency for Higher Education said: "It's hard to know the exact number of foreign students because the figures we receive from the universities relate to exchange students. There are no official national figures for the number of free movers yet."
Free tuition is a key reason for students coming to Sweden, suggests research by Anna Sjökvist and Lisa Wedin at Umea School of Business and Economics.
Mike MacIssac, an American studying at the Stockholm Institute of Education, said that it "was certainly a factor".
Eldridge Adolfo, a British/Zimbabwean masters student in political science at Stockholm University, said: "The minimal cost of education here compared with the UK, where I took my first degree, was a significant draw - that, and the fact I could study in English." In Sweden, many degrees and masters programmes are taught in English.