The National Highway Traffic Safety Administration says it has received 12 complaints of fires.
Five cars were destroyed. Eight of the fires occurred when the engine was turned off. No injuries have been reported.
The agency says there's an increasing trend of fires, with most of the complaints coming in the past year. NHTSA opened a preliminary evaluation on Oct. 11 and will try to find the cause of the blazes. Depending on the findings, a recall could be ordered.
The fires could affect 36,000 "S" models of the Mini Cooper, Cooper Clubman and Cooper Convertible, from the 2007 and 2008 model years.
A spokeswoman for Mini, which is owned by German automaker BMW AG, said Monday that the company is investigating the issue and cooperating with NHTSA.
The Associated Press contributed to this story.