Codey Herrmann, 20, briefly faced Melbourne Magistrates Court on Saturday wearing a green t-shirt as he sat with his head lowered in the dock.

The self-described aspiring rapper was arrested in Greensborough on Friday about 11.20am but a police charge sheet states he has "nil fixed place of abode".

His arrest follows an extensive investigation into Aiia's death after the discovery of her body near Main Drive and Plenty Road in Bundoora on Wednesday, January 16 about 7am.

Ms Maasarwe, 21, got off a route 86 tram only moments before she was attacked late the previous evening.

Herrmann is alleged to have assaulted and killed her at the same location, the court was told on Saturday.

The particulars of the rape charge have not been released, with the court told some of the "specific words" aren't yet known to the family.

A mental health assessment has also been requested for Herrmann.

He made no bail application and has been remanded in custody to appear in the same court on Monday.

Earlier on Saturday Prime Minister Scott Morrison and his family visited the Melbourne memorial where Ms Maasarwe's body was found.

"Later today I'm going to be meeting with her father; words will fail me, I'm sure, as one father to another," he told reporters.

"I think the country is very shaken by it but at the same time, as always, reaches out and seeks to comfort."

Floral tributes continue to be laid at the site after two vigils at nearby La Trobe University and in the Melbourne CBD.

The young student spent her final hours on Tuesday socialising with new friends and enjoying events in the city she'd called home for five months.

Australian Associated Press