11/18/2011 AT 05:00 PM EST
Joe Paterno, who was fired as head football coach
in the Penn State child sex-abuse scandal
, has a treatable form of lung cancer.
Paterno, 84, is undergoing treatment for the disease, which was diagnosed last weekend during a follow-up visit for a bronchial illness, and "his doctors are optimistic he will make a full recovery," his son Scott Paterno says in a statement given to the Associated Press
"As everyone can appreciate, this is a deeply personal matter for my parents, and we simply ask that his privacy be respected as he proceeds with treatment," the statement says.
The legendary coach lost his job after former assistant coach Jerry Sandusky was accused of
molesting eight boys over 15 years, both before and after his retirement in 1999.