In an effort to ease the situation, MEP Cecilia Wikström of the Liberal Party (Folkpartiet) is taking steps to make Sweden a more attractive option for foreign students, and one of the key points is a major extension on the ten-day rule.
"Ten days, isn't that outrageous? I think it's an embarrassment for my country. Germany has 18 months, the Netherlands has 12, and then it's a falling scale until Sweden at the bottom with ten days," she told The Local.
The new EU directive, introduced by Wikström, aims at extending this period to 18 months for all non-EU students who've completed their studies within the EU.
But the directive covers more than just extending the job-seeking time. It includes social benefits for students, full access to the labour market, as well as offering opportunities for a student's spouse or partner.
"We need to attract skilled people and make them stay. We need people. Today, they're heading to the places where they are more welcome, which includes countries like Australia, Canada, and even parts of India. We need to keep up in a globalized world," Wikström said.
Swedish universities have been feeling the pinch since tuition fees were introduced, with Linköping University seeing non-EU foreign student numbers drop from 400 in 2010 to just 60 in 2013. The trend has been similar in other universities, with the non-EU foreign student population of Mälardalen University College dropping from 250 to just 16 over the same period.
With the new directive, students wouldn't be limited to staying in Sweden either. Indeed, they could head anywhere in the EU to look for work, but Wikström admitted that she hoped people wouldn't stray from Sweden.
"You should really consider staying in the country that gave you the best education," she said, but added the EU's free movement is "a beautiful symbol of a united Europe".
"Foreign students contribute to growth and prosperity, to research, and to a more successful future for all of the EU," she said.
While Wikström works to change rules making it easier for foreign students to stay in Sweden upon completing their degrees, others say more needs to be done to attract non-EU students who now face a stiff bill for a Swedish education following the introduction of tuition fees.
In mid-January, for example, a group of industry and university heads argued
that the only way Sweden can compete internationally is to offer scholarships to entice more foreigners to enroll at the country's universities.