City officials say you should call 911 if you encounter anyone soliciting money on behalf of Allen. They say there have been reports of people going door-to-door with collection cans.
Allen died Friday, two days after he was injured fighting a house fire in the Hollywood Hills.
Allen's funeral is set for Friday at the Cathedral of Our Lady of the Angels in downtown L.A.
At the Hollywood Hills home where the fire occurred, Los Angeles Police put up crime tape Wednesday. The tape was set up to further preserve the site of the ongoing investigation.
Chief Michael Greenup of the LAFD's Arson Unit said the LAPD is assisting the fire department in their investigation of the death of firefighter Glenn Allen.
According to Greenup, the fire has been ruled accidental.