While the driver, a 32-year-old Australian citizen, was known to police for minor traffic offences and a minor assault in 2010, police say he also had a history of drug use and mental health issues.
"Doctors will determine when he is fit for interview," Victoria Police Acting Chief Commissioner Shane Patton told press, as reported by SMH. "We will be hoping to interview him at the earliest possible stage.
While investigators have not been granted access for an official interview, they have had preliminary discussions with him, according to Patton.
"During those discussions, he made some utterances … in respect to a number of matters. He spoke of dreams and voices, but also attributed some of his activities as well due to the mistreatment of Muslims.
"Now, obviously we are continuing to explore this entire incident and trying to ascertain what the motivations are.
"We haven't ruled anything in or out and our counter-terrorism command continues to obviously assist Crime Command in this investigation."
Four people are currently in a critical condition after being struck by the man’s white SUV on Flinders Street at Elizabeth Street. The off-duty police officer who arrested the man is also in hospital.
"He [the off-duty officer] deserves special praise for the way in which he instinctively came to the rescue of others avoiding so much further carnage," Victorian Premier Daniel Andrews said.
"We have to be strong, we have to continue on as a community... come in, go to the carols, go to the cricket," he said.