According to the London police statement, the incident occurred in the evening of 27 February.
The attacker poured a liquid, thought to be gasoline, on the man and lit it with a lighter.
The police demanded support for the search efforts by sharing the images of the attacker.
Detectives said that before the attack, both the attacker and the victim were seen leaving the West London Islamic Center on Singapore Road in Ealing and chatted for about five minutes.
After the conversation, the attacker set the 82-year-old man on fire.
The old man suffered severe burns on his face and arms and was taken to the hospital.
Detective Sergeant Steven Constable urged anyone who knew the suspect to contact the police.