Outspoken independent senator Derryn Hinch will move a motion next week calling for private schools to be stripped of public funding if they exercise their right to exclude gay students or teachers.

Religious schools already have exemptions to discrimination laws that allow them to exclude gay people in several states, including NSW, but not in others like Queensland.

The government-commissioned Ruddock review, leaked in part on Wednesday, recommends enshrining the exemption in federal law.

“I will move a notice of motion in the Senate [on] Monday calling for any private school that discriminates against a teacher or student on sexuality grounds be stripped of all government funds and charity status,” Senator Hinch wrote on Twitter.

“Schools cannot discriminate against a child or a teacher on the grounds of sexuality. It’s just immoral,” he then told a radio station.

Prime Minister Scott Morrison has downplayed the significance of the leaked report, saying the exemptions were an “existing law”.

The existing federal law does say it is not “unlawful” to discriminate against someone for their sexuality, gender identity or pregnancy “in connection with the provision of education”.

The government has pointed out the recommendations would actually tighten some of the exemptions, compared with the absolute rights enjoyed by some states now.

It would no longer be legal to discriminate based on pregnancy, and schools would be forced to publish their hiring policy.

“We weren't suggesting that the law should be expanded, we were suggesting it should be contracted to ensure that information was clear and unambiguous to those who were seeking to enrol children,” the report’s lead author, Liberal elder Philip Ruddock, told ABC Radio.

The report is yet to be released to the public and the government is still considering its response.

Among the most significant recommendations is the proposal for a new Religious Discrimination Act, that would make it illegal to discriminate against someone on the basis of their religious beliefs.

That would make beliefs a protected attribute, like gender, race and disability are now.