The one-time Anfield supremo wants tougher prison sentences and a new anti-corruption unit to prevent gambling on sport leading to match-fixing, after chairing a review into betting.
The proposed unit, called the Sports Betting Intelligence Unit, would be housed within the Gambling Commission.
The review was commissioned by sports minister Gerry Sutcliffe following increasing concerns about betting on sport leading to cheating.
Parry said: 'There is no great evidence at the moment that corruption is endemic, but just one problem can have a huge impact on a sport so there is no room for complacency.
'We have to take the toughest possible approach if we want to stamp out cheating.'
Parry believes the current two-year maximum prison term for cheating on sports gambling is too lenient.
He added: 'This is potentially a very serious offence and more severe sanctions would put it higher on the police's radar.'
Parry said it was unrealistic for the UK to move to the American system where almost all betting on sport is banned.