The newspaper Svenska Dagbladet has interviewed several members of the party and claims that its leadership, generally viewed as more liberal and pro-market, does not prioritise a review in the school law.
The more left-leaning members and those with ties to labour unions believe profit-making should be banned in state-funded "free schools", the terminology used in Sweden to describe a charter school.
The party's education policy spokesperson Ibrahim Baylan denies that disagreements have caused any ill-will within the party. He also says the real issue is not whether private actors make a profit, but where the profit goes.
"What upsets a lot of people, and justifiably so," says Baylan, "is that the money disappears in different ways and, in general, isn't used in the way it should be."
The party leader, Stefan Löfven, has previously said any surplus income should be reinvested in the schools.