However, the National Association of School Governing Bodies has defended the role it plays in appointing principals.
"We vehemently oppose that sentiment because we feel everybody, as long as the laws allow, should play a role in the appointment of principals," the association's general secretary, Matakanye Matakanye, said.
He said if the governing bodies didn't play a role, principals would be imposed on schools.
"The SGBs recommend to the director-general a person who we believe is capable to lead our schools, and that should continue," Matakanye said.
Lesufi has had to put out fires at a number of Gauteng schools recently following disputed appointments of principals, including at Klipspruit Secondary School.