The young adult male whale was discovered Monday morning on Little Dume beach between Paradise Cove and Point Dume, KTLA-TV, Los Angeles, reported.
Officials with the city of Malibu assumed Los Angeles County would handle the removal of the whale carcass, but county officials said Little Dume is a private beach and therefore not its responsibility.
The Los Angeles Times reported the beach is not private.
The state could take care of the rotting carcass, though the nearest state property is about a mile away from Little Dume, KTLA reported.
"There have been some issues with jurisdiction," said Los Angeles County Fire Inspector Quvondo Johnson.
Because of how long the whale has been decomposing, towing the carcass back out to sea would be impossible.
"It'll just break apart and make a big mess," said Roy Stearns, a spokesman for the California Department of Parks and Recreation.
A necropsy performed on the animal Tuesday found the whale suffered a gash on its back and damage to its vertebrae, KTLA reported.
Fin whales are the second-largest whales next to blue whales, and can grow to be 85 feet long.