Labor says the government will break another election promise if it pursues plans to open $6 billion of university funding to private sector competition.

Labor higher education spokesman Kim Carr said that would mean less money for students of existing institutions, which the government clearly promised it wouldn't do before the election.

Kim Carr Credit:Alex Ellinghausen

News Ltd newspapers have reported that the government is considering opening the $6 billion Commonwealth Grants Scheme to private institutions and non-university institutions such as TAFE colleges.

Currently there are just three private universities in Australia. That compares with the US where a fifth of all students attend private universities, including some of the country's most esteemed institutions.