THE mother of a teenage boy who police believe was preparing to carry out a public beheading on an Australian street did not report her son to police, despite him apparently boasting that he wanted his attack to be "bigger" than the murder of police worker Curtis Cheng.

News Corp is reporting that court documents show the 16-year-old boy, who is facing terror-related charges with another teenager, had told his mother he wanted to do "something to them that they have never seen before".

The accused teen also took part in a violent Hyde Park protest alongside other radicals in 2012, when he would have been 12. He was holding a sign calling for the beheading of anyone insulting the prophet.

At no point did the boy's mother contact police about her son's radical beliefs, News Corp reports.

She was in Parramatta Children's Court as her son's case was heard on Thursday.

The two teenagers are charged with carrying out an act done in preparation for a terror attack and membership of a terrorist organisation.

The former charge can carry a life sentence.

Police arrested the two boys less than an hour after they allegedly bought two M9 bayonets.