The issue is a controversial one and municipalities have complained that the regulations are not crystal clear on whether the children, who follow their families to Sweden where they eke out a living by begging on the streets, have a right to an education.
The Liberal Party's economics spokesman Erik Ullenhag tells Swedish Radio that the youngsters are typically taken out of school in their home country and brought to Sweden for only a short time, thus disrupting their studies.
Christina Höj Larsen, spokeswoman on migration issues for the Left Party, is critical of the proposal. She says the Liberal Party's suggestion is unrealistic and that a child in Sweden has a right to go to school.
Local governments are not currently required to admit the children of EU migrants, many of whom come from Romanian and overstay the 3-month limit to remain unconditionally in Sweden, but some municipalities such as Gothenburg are letting them attend school if they ask.
The Liberal Party does not want to ban municipalities from admitting the children though Ullenhag says it's not an ideal solution.
"The best is to make sure we can help schools in Romania get better, but also that children have the right to attend school (in the country) where they primarily live," he says.