A silver VW Golf was sent up in flames in Hudson Road, Harehills on Thursday, August 16, just outside the famous Montague Burton factory.
Police were contacted at 4.33pm by the fire service who believed the fire had been started deliberately.
The vehicle was significantly damaged by the fire and the heat also caused damage to the windows of business premises that the car was parked outside.
Police officers attended the scene and viewed CCTV that showed two suspects – a black male and a white male on a scooter – approached the vehicle at about 4.15pm.
The first suspect, who had his face covered, poured liquid onto the vehicle and set it alight before both males left the scene
The footage was not clear enough to identify them.
A West Yorkshire Police spokesperson said: "At 4.33pm yesterday (16/8) police were contacted by the fire service who were attending a car fire in Hudson Road, Harehills.
"A silver VW Golf had been significantly damaged by fire. The heat of the fire also caused damage to the windows of business premises that the car was parked outside.
"Firefighters believed the fire had been started deliberately and crimes of arson and criminal damage were recorded.
"Anyone who witnessed the incident or who has any information that could assist in identifying the suspects is asked to contact officers via 101 quoting crime reference 13180407643, or contact the independent charity Crimestoppers anonymously on 0800 555 111."