Beckenbauer, who won the World Cup with West Germany as both a player and coach, said that although Rooney was universally recognised as a "brilliant player" before this season, he had taken his game to new heights.
"He is doing an absolutely fantastic job for Manchester United and I must tell you that we at Bayern will fear him when we play United in the Champions League quarter-finals," Beckenbauer told Reuters.
"But at the same time, he is a brilliant player who is playing better than ever. It is not easy to score 33 goals for your club in England, or anywhere else, and if he continues scoring like that and playing like that he can win the World Cup for England," said Beckenbauer, who is attending the annual UEFA Congress in his role as a FIFA executive committee member and is also honorary president of Bayern Munich.
"I think they go to South Africa among the favourites along with Spain, Brazil, Argentina, because, of course, Argentina have Lionel Messi who along with Rooney is the best player in the world right now.
"They are different players because Messi is so fast and imaginative while Rooney is so strong, but Wayne has made the biggest improvement to his game. He has changed the way he plays and, at 24, has added a maturity to his game.
"Playing as the front man, he makes it so hard for defenders to mark him and he is able to use the crosses from both wings so well. I have never seen him play better and I have been watching him for a long time now."
Beckenbauer said Rooney would be a major factor for Bayern in the Champions League quarter-final.
"We have a very difficult and busy League and Cup programme going into that tie," he said.
"Of course we would like to knock them out for revenge for losing the 1999 final but it is going to be tough, and, of course, United have Rooney. Anything is possible but first we have to stop Wayne and no-one has been able to do that very often this season."
Bayern host United in the first leg next Tuesday, with the return leg on April 7.
Follow FFT.com on Twitter
Join FFT.com on Facebook
