The former Chelsea star believes the Manchester United striker is the best player in Roy Hodgson's squad and has urged him to make the 28-year-old the focal point of the team
Rooney was widely criticised for his performance in England's 2-1 loss to Italy, but scored his first ever World Cup goal against Uruguay on Thursday, though he could not prevent the Three Lions from losing by the same scoreline again.
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Writing for The Times, the ex-Germany international said: "For me the only player who looked like making a difference for England was Rooney. He is the only one who can hurt teams, and the only one who is really world class.
"Some people are saying he should be dropped, which is crazy. He should always play through the middle, as asking him to move out wide is a waste of time. He's the best player and should have the freedom to play.
"Despite all these problems, England look better than they did two years ago and Roy Hodgson should build the team around Rooney and tell his team to do everything they can to play for him."
Ballack also criticised Steven Gerrard, who was at fault for Luis Suarez's winner in Sao Paulo, claiming the Liverpool midfielder simply "passes from side to side" when he plays for his country.
"I'm always impressed when I watch Steven Gerrard for Liverpool — as I was when I played against him for Chelsea — but he's not the same player for England," Ballack added.
"He just doesn't have the same influence on matches. He should have the same standing as he is the captain in both teams, but with England he is not the same.
"It may be because he has — and feels — too much responsibility. At Liverpool he has other players to do the running for him so he can concentrate on organising his team-mates and there is a shared responsibility. He is playing within a clear structure and to a set philosophy, which brings the best out of him.
"When Gerrard plays for England he just passes the ball from side to side. He doesn't get forward. Maybe he's tired now after a difficult season, but it has been a problem for a while."