The human remains that have been washing up along the Maribyrnong River are believed to belong to a Melbourne man aged in his late 30s, who was not a missing person.

The possible breakthrough was made when a close member of the man's family identified a tattoo of a devil on his forearm, which police released through the media last week.

Police investigating the death of Brendan Bernard take away evidence from the banks of the Maribyrnong River. Credit:Chris Hopkins

That family member walked into the North Melbourne police station and told police they had recognised the tattoo, detective inspector Mick Hughes said on Sunday.

"It's a tragic way for the family to find out but it has progressed our investigation," he said.