Jay Cooper, an attorney for Horner, said the plane was one of several owned by the 61-year-old composer, and that no one has heard from him since the crash.
"It was his plane and if he wasn't in it, he would've called," Cooper said Monday night.
The Associated Press has not confirmed Horner's death.
The Hollywood Reporter cited Sylvia Patrycja, who it says is identified on Horner's film music page as his assistant in confirming his death. She wrote on Facebook on Monday, "We have lost an amazing person with a huge heart and unbelievable talent. He died doing what he loved. Thank you for all your support and love and see you down the road."
The AP was not immediately able to independently confirm the veracity of the post.
The single-engine plane crashed Monday morning in the Los Padres National Forest, Ventura County fire spokesman Mike Lindbery said.
The pilot was killed. No one else was on board.
The plane was an S-312 Tucano MK1 turbo-prop with two seats, said Ian Gregor, spokesman for the Federal Aviation Administration.
Crews extinguished a fire that erupted in vegetation surrounding the remote crash site, about 100 miles northwest of Los Angeles.
Horner has been nominated for 10 Academy Awards, winning two for 1997's best picture, "Titanic." He composed the film's score and its enduring theme song, "My Heart Will Go On," sung by Celine Dion.
His scores for "Alien," ''Apollo 13," ''Field of Dreams," ''Braveheart," ''A Beautiful Mind," ''House of Sand and Fog" and "Avatar" also earned Oscar nods, as did his original song, "Somewhere Out There," from "An American Tail."
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