Flinders Street driver Saeed Noori rambled about Allah, Australia's spy agency ASIO and the mistreatment of Muslims in the hours after the attack, police say.

Police revealed more on Friday afternoon about what the 32-year-old drug addict told them as investigators continue to search for a motive behind the rampage.

It comes as Mr Noori was discharged from hospital and into police custody, where he is set to spend the night before being formally interviewed by homicide detectives on Saturday. He has not yet been charged.

Acting Chief Commissioner Shane Patton said police have not ruled out terrorism, but the only clue that suggested a possible link was what Mr Noori told investigators in St Vincent's Hospital on Thursday night.