The suspect, Luka Rocco Magnotta, who is awaiting extradition from Germany to Canada, is accused of having killed and dismembered a Chinese man in Montreal, and then sending his body parts to political parties and schools.
Investigators from Montreal's serious crimes unit "know that Magnotta was on the US West Coast," police spokesman Ian Lafreniere told AFP, adding that it was not clear whether he stopped in Los Angeles or was in another coastal city.
The head, hands and feet of 66-year-old Hervey Medellin were found in a Los Angeles park in January.
Montreal investigators have not yet coordinated with the Los Angeles police on an investigation, as they are handling the around-the-clock probe into the gruesome demise of the Chinese student, Lin Jun.
"We know that our suspect (Magnotta) was someone who traveled a lot. We are trying to retrace his route, see where he went. It's not easy," Lafreniere explained.
Canadian authorities are still waiting for the results of DNA tests from Magnotta, who was arrested on Monday in an Internet cafe in Berlin.
Meanwhile, the British tabloid The Sun reported that a pimp identified as Alex believed that Magnotta was working as a prostitute in Los Angeles at the time of Medellin's killing.
The paper said that weeks after the discovery of Medellin's body, Magnotta was offering massages to male clients on his Facebook page from an apartment in Hollywood.
© Copyright AFP Agence France-Presse GmbH - All rights reserved. This material may not be published, broadcast, rewritten or distributed. All reproduction or redistribution is expressly forbidden without the prior written agreement of AFP.