Osborne played his high school football at Robert E. Lee High School in San Antonio where he earned all-state honors as a wide receiver. He helped lead the Lee Volunteers to a 28-27 1971 UIL 4A State title over Wichita Falls high school. Tommy Kramer who had a long NFL career was his quarterback in high school. Another notable teammate in high school was Pat Rockett who also earned all-state honors and later played Major League Baseball for the Atlanta Braves.