The U.S. Forest Service said an off-duty ranger found the bones in the northeastern end of the park, the Contra Costa (Calif.) Times reported Tuesday.
Authorities say DNA tests will be conducted to see if they are the bones of Fred Claassen, an experienced hiker who embarked on a 20-mile trail trek in July 2003.
After he was reported missing, his car was found at the Twin Lakes trail head in the park. An extensive search at the time turned up no trace of Claassen.
The Inyo Register reported Claassen's belongings, including a wallet and camera, were found near the remains and that the hiker died from a fall; but Kari Cobb, a Yosemite park ranger and spokeswoman, said the park would neither confirm nor deny that reports until the remains are positively identified.