The Oklahoma Highway Patrol confirmed it investigated the Sunday crash 5 miles north of the Tulsa International Airport, the television station said.
The World said government records indicated the younger Inhofe was associated with a company that recently bought the plane.
Inhofe, 52, was an orthopedic surgeon in Tulsa, and was a licensed pilot and flight instructor, the World said.
Tulsa International Airport officials said the pilot issued an alert Sunday afternoon, asking for immediate assistance. The plane crashed about 15 minutes after the alert.
Oklahoma Highway Patrol spokesman George Brown confirmed one person died in the crash, saying there could have been more than one fatality, but authorities only saw evidence of one, the World said.
Brown said the National Transportation Safety Board and FAA had taken the lead on the crash.
He said it could be days, or even weeks, before authorities release the name of the victim. Amy Elliott, Oklahoma Medical Examiner's Office spokeswoman, said the office's identification of the pilot would not be possible until dental records it requested were received.
Another pilot, Justin Allison of Tulsa, was flying minutes behind the aircraft that crashed, and told the World he heard air traffic controllers report a plane ahead of him had experienced engine failure. He also was directed to climb from 2,500 feet to 5,000 feet and remain in a holding pattern.
"I couldn't hear the pilot, but I heard the tower declare an emergency for him," Allison said, "which is a red-flag raiser, because usually the pilot will declare the emergency."