More body parts believed to belong to slain Melbourne man Brendan Bernard have been found near the Maribyrnong River, weeks after the first grisly find.

Senior Constable Adam West said a member of public found the body parts about 4pm on Sunday.

Brendan Bernard, whose severed forearm was found in the Maribyrnong River on February 5, 2015.

"We suspect they'll be from the deceased Brendan Bernard," he said.

Mr Bernard's dismembered limbs began surfacing in the Maribyrnong River in early February, among them a forearm decorated with a distinctive devil tattoo, which was found by a walker.