The Cole fire has often smouldered rather than exploded into flames and Rush believes it's time for the 29-year-old to deliver.
"With the talent he has, Joe doesn't want to be known as a nearly man," Rush stated. "I am sure that playing regularly with Liverpool will give him the chance to prove he is a really top, top-class player. He can become a hero to The Kop.
"He can change games and I was baffled when England didn't really give him a chance in the World Cup finals.
"It was a big step for him to move up to Liverpool, something the fans appreciate. They are anxious for him to do well."