Shire Ali killed much-loved restaurant owner Sisto Malaspina and severely injured two others after he drove his ute – filled with barbecue gas cylinders – into the middle of Melbourne's CBD, before setting the vehicle alight and going on a stabbing rampage.

In the early hours of Saturday, federal police raided the Meadow Heights property where Shire Ali had been living with his wife.

The owner of the property said on Monday they had allowed Shire Ali’s wife and child to move into the converted garage about six months earlier.

At the time a family friend, Shire Ali’s father-in-law, revealed his daughter was separated from her husband.

“We offered to help her,” the owner said.

“But about two months ago he moved in.

“We were waiting for her father to fly back from Turkey so we could tell him she needed to go now they were together again."

She said Shire Ali's father-in-law was due to fly back to Australia on the same day as the Bourke Street attack.

The woman said she knew the young mother as a friendly woman who dressed conservatively, but had concerns about her husband.

“She is such a beautiful girl and never did anything out or the ordinary,” she said

“Her father though had begun worrying about the way she was dressing.

“He didn’t like her husband ... we’d had problems with him too.”

The woman said Shire Ali had woken up her elderly mother one night by banging on the door at 11.30pm.

“He said he wanted to speak to the man of the house,” she said.

“I told him that’s me but he came across as crazy. If only we’d known.”

The woman's mother, who lives permanently at the Meadow Heights home, said she was still shocked by Friday's events.

On Monday, broken glass remained scattered across the driveway following the police raid.

Children’s toys, including a green ride-on car and soccer ball, were visible in the living room through a window, while a pressure washer was in the concrete courtyard outside.

Police have said Shire Ali, who arrived in Australia as a child with his parents in the 1980s from Somalia, held radical views and was known to federal counter-terrorism agencies.

His passport was seized in 2015 when he made plans to travel to Syria.

"He's got family associations that are well known to us," Police Commissioner Graham Ashton said on Friday night.

Shire Ali also had a criminal history for cannabis use, theft and driving offences, Mr Ashton said.

Acting deputy commissioner for national security Ian McCartney said that while Shire Ali did not have direct contact with Islamic State, authorities believe he was inspired by the extremist organisation.

"It's fair to say he was inspired. We're not saying it was direct contact, we're saying it's from an inspiration perspective," Mr McCartney said.

Fairfax Media revealed on Saturday that Shire Ali also believed he was being chased by "unseen people with spears" as he grew increasingly agitated and delusional in the weeks before he went on the deadly rampage.

On Saturday, his parents' home – a modest brick house on a quiet street in Werribee, in the city's west – was also raided in early on Saturday by police, who were there for more than 12 hours.

Sources close to his family said he had a troubled relationship with them and his life had "spun out of control" in recent years, as he grappled with mental-health issues and substance abuse.