Until now this has been opposed by the largest party, the conservative Moderates, as well as by the Christian Democrats.
But now the Christian Democrats say to Dagens Nyheter that they share the view of the Center and Liberal parties on this issue.
Michael Arthursson will become the Centre Party's general secretary from next year. He says that his party has seen this as an important issue for a while, and wants to act on it before the next election looms.
"We have a society where people ask for more openness, especially from politicians and on things that are important to people."
"We think there is much to win for everyone involved, by having more openness."
He says that the reason the Center Party had not moved to change the rules before is that there was, in the past, a different culture, where it was accepted that companies could fund political parties anonymously.
Nicholas Aylott is a political scientist at Södertorn University, to the south of Stockholm.
He says that there are three reasons why no rules have been brought in before - firstly that parties are seen as part of civil society, rather than public authorities; plus Sweden's reputation for transparency has meant that no one has thought of applying this regulation to political parties. The most important reason, he says, is that there has been a tacit agreement between the biggest parties - the Social Democrats and the Moderates.
"Everyone knows that the labour movement contributes a lot of money and manpower to the Social Democrats, it's no secret - but any kind of regime that would try to regulate it would be very expensive and time consuming, and the Social Democrats are very keen to avoid that exercise."
And the Moderate party receives a lot of donations from completely unknown sources - about $US 10 million every year.