A confirmation of the man's identity is expected on Tuesday when forensic results are returned after a person, believed to be a relative, came forward.

But investigators are tracing the man's final movements, trawling through a vast amount of information that has come from people who say they saw suspicious activity along the river in the lead-up to the discovery of the body parts on Thursday.

Police returned to the river on Monday, for the fifth day in a row, to search a small section at Moonee Ponds in Melbourne's inner-west for missing remains.

The police boat travelled between the points where unsuspecting walkers and rowers have found body parts in plastic bags that have washed-up on the river's banks.

The area covers about four kilometres between the footbridge at Afton Street, The Boathouse cafe, Anglers Tavern and just south of the Raleigh Road bridge.

Homicide Squad Detective Inspector Mick Hughes said on Sunday a close relative of the suspected victim came forward after police released an image of a devil tattoo found on a forearm, the first limb discovered on Thursday.

The relative walked into the North Melbourne police station and told officers they recognised the tattoo.

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

Inspector Hughes said police expect to release the name of the victim once he is formally identified through the DNA testing.

It is believed the man was not known to police. He had last been in contact with his family during the Christmas period and was not listed as a missing person.

The tattoo bears a striking resemblance to cover art used on a Sydney punk band's album but the devil depicted in the tattoo holds a spray can instead of a bouquet.

The hardcore punk band Downtime gained some prominence in the 1990s, playing at the Big Day Out in 1994 and finding some success with their second album Tooth and Nail in 1997, which bears the devil on the cover.

Police said the man found in the Maribyrnong is not connected to the band after they spoke to their manager. Those connected to Downtime said the cover art was based on a picture they found in a magazine.

Anyone with information should phone Crime Stoppers on 1800 333 000 or submit a confidential report to www.crimestoppersvic.com.au.