U.S. auto safety regulators are investigating reports that the engines can catch fire on some Jeep SUVs and pickup trucks even with the ignition turned off.

The probe covers more than 781,000 Jeep Wrangler and Gladiator vehicles from the 2021 through 2023 model years.

The National Highway Traffic Safety Administration says in documents posted Monday on its website that it has nine complaints of engine fires from owners including one that caused an injury. A majority of the reports say fires began in the passenger side of the engine compartment.

The agency says a fire with the ignition off "can result in an increased risk of occupant injury, injury to persons outside the vehicle, and property damage, with little or no warning."

Investigators contacted Jeep maker Stellantis and were told of several other "thermal events" that started at a power steering pump electrical connector.

The agency said it's opening the investigation to determine the cause and scope of the problem and how often it happens. No recall has been issued, but one is possible.

Stellantis said it is cooperating with the investigation.

Michael Brooks, executive director of the nonprofit Center for Auto Safety, said it would be wise for owners of the Jeeps under investigation to park them outdoors until the matter is resolved because NHTSA is citing a risk of property damage.

"If I owned one of these vehicles, I certainly wouldn't want to park it in a garage," Brooks said.