Family members have told a number of Calgary-based media outlets that the 67 year old had a heart attack in his sleep and was taken to Eisenhower Medical Center in Palm Springs.
Tom Forzani says doctors have told them his brother is unlikely to recover.
John was an offensive lineman for six years with the Stampeders in the 1970s, where he played alongside his brothers Tom and Joe.
After he retired from football, John Forzani built a chain of successful sporting goods stores.
That chain, FGL Sports, was sold to Canadian Tire in 2011.
John established Calgary's annual Mother's Day Run and Walk in 1977, a fundraising event which continues to this day. In 2000, the Forzani Foundation was established to assist charities including Canadian amateur athletics.